vania-janet/multiturn-rag-retrieval-data huggingface dataset:
you should always invest if your investment rate of return is higher   than your interest rate Your next line, about standard deviation is dead on.  There are too many variables to give an exact answer here, in my opinion. The main reason is that one variable isn't easy to quantify - One's risk tolerance.  Clearly, there's one extreme, the 18% credit card. Unless you are funding loanshark type rates of 2%/week, it's safe to say that 18% debt should take priority over any investments, except for the matched 401(k) deposits.  What I think you're talking about is something we've addressed here in multiple threads.  Do I prepay my sub 4% mortgage or invest? In this case, (and to Noah's comment) the question is whether you can expect a post-tax return of over 3% during your time horizon. I look at the return for 15 years from 1998-2013 and see a 6% CAGR for the S&P. I chose 15 years, as the choice is often one of paying a 30 year mortgage faster, as fast as 15. The last 15 years offer a pretty bad scenario, 2 crashes and a mortgage crisis. 6% after long term gains would get you 5.1% net.  You can pull the data back to 1871 and run CAGR numbers for the timeframe of your choosing. I haven't done it yet, but I imagine there's no 15 year span that lags the 3% target I cite.  What makes it more complex is that the investment isn't lump sum. It may not be obvious, but CAGR is a dollar invested at T=0, and returns calculated to T=final year. It would take a bit of spreadsheeting to invest the extra funds every month/year over your period of analysis.  In the end, there are still those who will choose to pay off their 4% mortgage regardless of what the numbers show. Even if the 15 year result showed worst case 3.5% (almost no profit) and an average 10%, the feeling of risk is more than many will want.
This is because the cap rate exceeds the note rate (4.974 % APY vs. 4.594 % APY), and the leverage decreases from 5x to 1x. The weighted average compound annual growth rate of the equity during the 30 years is 5.511 % APY. Per the original poster's answer, this is computed by taking the 30th root of the 5-fold increase in equity. Because the owner made no extra principal payments (besides those already discussed), the relevant amounts are the initial $ 40,000 owner payment and the final $ 200,000 owner equity. 5.511 % APY corresponds to a 5.377 % APR. The internal rate of return if the owner never sells can be computed by treating the deal as a $ 40,000 up-front payment, in exchange for an $ 810.70 monthly payment starting in 30 years. The internal rate of return (IRR) is not a very useful number, because it assumes that you can somehow reinvest the eventual dividends at the same rate. In this example, the IRR is 5.172 % APR, or 5.296  % APY. In this example, the IRR is calculated by (iteratively) finding an interest rate for which (initial investment) * (1 + IRR) ^ (number periods before dividends start) = (periodic dividend) / (IRR - growth rate of dividend). For example: $ 40,000 * (1.004309687)^360 = $ 810.70 / (0.004309687 - 0) = $ 188,111 I then converted the 0.431 % monthly IRR to an annual IRR. The deal can be thought of as a return on equity, plus a return on paying down the mortgage. When computing the return from paying down the mortgage, the initial equity is irrelevant. It does not matter whether you start with a $ 160,000 mortgage on a $ 160,000 property, a $ 160,000 mortgage on a $ 200,000 property, or a $ 160,000 mortgage on a $ 1,000,000 property. All that matters is the note rate on the mortgage, which is the applicable compound interest rate.
"The short answer is: banks are less concerned about the interest earned on any single mortgage than they are for the interest earned over time from a collection of mortgages. Let's look at a repayment schedule for a 30-year mortgage at 4% for $100,000. (source: http://web5.vlending.com/loancenter-calculators-amort.aspx. Any mortgage calculator should produce a similar schedule, however.) A few things to note: The interest due in the last 6 years is less than the interest due in the first year alone. Banks are getting a disproportionate amount of the expected interest up front. Banks can make multiple loans; the money collected from existing borrowers can be aggregated to make new loans before the old ones are paid off, and those new loans start, of course, at the interest-heavy end of the repayment schedule. Suppose the bank lends out $1,000,000 to 10 borrowers. In the first two years, they will collect a total of $114588.90 from the 10 borrowers in principal and interest. That's enough to make an additional loan to an 11th borrower while keeping $14,588.90 as ""profit"". The new borrower is making payments at the year-one rate. A bank may lose a little interest on a single loan that gets repaid early, but that is generally made up by the fact that a new loan can be issued that much sooner as a result."
It depends on the relative rates and relative risk. Ignore the deduction. You want to compare the rates of the investment and the mortgage, either both after-tax or both before-tax. Your mortgage costs you 5% (a bit less after-tax), and prepayments effectively yield a guaranteed 5% return. If you can earn more than that in your IRA with a risk-free investment, invest. If you can earn more than that in your IRA while taking on a degree of risk that you are comfortable with, invest. If not, pay down your mortgage. See this article: Mortgage Prepayment as Investment: For example, the borrower with a 6% mortgage who has excess cash flow would do well to use it to pay down the mortgage balance if the alternative is investment in assets that yield 2%. But if two years down the road the same assets yield 7%, the borrower can stop allocating excess cash flow to the mortgage and start accumulating financial assets. Note that he's not comparing the relative risk of the investments. Paying down your mortgage has a guaranteed return. You're talking about CDs, which are low risk, so your comparison is simple. If your alternative investment is stocks, then there's an element of risk that it won't earn enough to outpace the mortgage cost. Update: hopefully this example makes it clearer: For example, lets compare investing $100,000 in repayment of a 6% mortgage with investing it in a fund that pays 5% before-tax, and taxes are deferred for 10 years. For the mortgage, we enter 10 years for the period, 3.6% (if that is the applicable rate) for the after tax return, $100,000 as the present value, and we obtain a future value of $142,429. For the alternative investment, we do the same except we enter 5% as the return, and we get a future value of $162,889. However, taxes are now due on the $62,889 of interest, which reduces the future value to $137,734. The mortgage repayment does a little better.
One thing you didn't mention is whether the 401(k) offers a match. If it does, this is a slam-dunk. The $303 ($303, right?) is $3636/yr that will be doubled on deposit. It's typical for the first 5% of one's salary to capture the match, so this is right there.  In 15 years, you'll still owe $76,519. But 15 * $7272 is $109,080 in your 401(k) even without taking any growth into account. The likely value of that 401(k) is closer to $210K, using 8% over that 15 years, (At 6%, it drops to 'only' $176K, but as I stated, the value of the match is so great that I'd jump right on that.) If you don't get a match of any kind, I need to edit / completely rip my answer. It morphs into whether you feel that 15 years (Really 30) the market will exceed the 4% cost of that money. Odds are, it will. The worst 15 year period this past century 2000-2014 still had a CAGR of 4.2%.
Do you think your 403b will earn more than the mortgage interest rate?  If so, then mortgage seems the way to go. Conservative investment strategies might not earn much more than a 3-4% mortgage, and if you're paying 5-6% it's more likely you'll be earning less than the mortgage. From another point of view, though, I would probably take a loan anyway just from a security standpoint - you have more risk if you put a third of your retirement savings into one purchase directly, whereas if you do a 10-15 year loan, you'll have more of a cushion.  Also, if you don't outlive the mortgage, you'll have had use of more of your retirement income than otherwise - though I do wonder if it puts you at some risk if you have significant medical bills (which might require you to liquidate your 403b but wouldn't require you to sell your house, so paying it off has some upside). Also, as @chili555 notes in comments, you should consider the taxation of your 403(b) income.  If you pull it out in one lump sum, some of it may be taxed at a higher rate than if you pulled it out more slowly over time, which will easily overwhelm any interest rate differences.  This assumes it's not a Roth 403(b) account; if it is Roth then it doesn't matter.
Keep in mind, this is a matter of preference, and the answers here are going to give you a look at the choices and the member's view on the positive/negative for each one.  My opinion is to put 20% down (to avoid PMI) if the bank will lend you the full 80%. Then, buy the house, move in, and furnish it. Keep track of your spending for 2 years minimum. It's the anti-budget. Not a list of constraints you have for each category of spending, but a rear-view mirror of what you spend. This will help tell you if, in the new house, you are still saving well beyond that 401(k) and other retirement accounts, or dipping into that large reserve.  At that point, start to think about where kids fit into your plans. People in million dollar homes tend to have child care that's 3-5x the cost the middle class has. (Disclosure - 10 years ago, our's cost $30K/year).  Today, your rate will be about 4%, and federal marginal tax rate of 25%+, meaning a real cost of 3%. Just under the long term inflation rate, 3.2% over the last 100 years. I am 53, and for my childhood right through college, the daily passbook rate was 5%. Long term government debt is also at a record low level. This is the chart for 30 year bonds.  I'd also suggest you get an understanding of the long term stock market return. Long term, 10%, but with periods as long as 10 years where the return can be negative.  Once you are at that point, 2-3 years in the house, you can look at the pile of cash, and have 3 choices.  We are in interesting times right now. For much of my life I'd have said the potential positive return wasn't worth the risk, but then the mortgage rate was well above 6-7%. Very different today.
"The advice to pay off near-7% debt is tough to argue against. That said, I'd project out a few years to understand the home purchase. Will you plan for the 20% down John recommends? The Crazy Truth about PMI can't be ignored. The way the math works, if you put 15% down, the PMI costs you so much, it's nearly like paying 20% interest on that missing 5%.  If your answer is that you intend to save for the full downpayment, 20%, and can still knock off the student loan, by all means, go for it. I have to question the validity of ""we will definitely be in a higher tax bracket when we retire."" By definition, pretax deposits save tax at the marginal rate. i.e. If you are in the 25% bracket, a $1000 deposit saves you $250 in tax that year. But, withdrawals come at your average rate, i.e. your tax bill divided by gross income. There's the deductions for itemized deductions or the standard. Then 2 exemptions if you are married. Then the 10% bracket, etc.  Today, a couple grossing $100K may be in the 25% bracket, but their average rate is 12%.  I read this Q&A again and would add one more observation - Student Loans and Your First Mortgage is an article I wrote in response to a friend's similar question. With the OP having plan to buy a house, paying off the loan may be more costly in the long run. It may keep him from qualifying for the size mortgage he needs, or from having enough money to put 20% down, as I noted earlier.  With finance, there are very few issues that are simply black and white. It's important to understand all aspects of one's finances to make any decision. Even if thee faster payoff is the right thing, it's not a slam-dunk, the other points should be considered."
I'm calculating that to about a 7% apr, which given loan rates available today seems a bit high.   I wouldn't get too caught up on what that equates to over the life of the loan.  There are a lot of forces in play over a 30 year period, namely the time value of money.  30 years from now a dollar will be less valuable in real terms due to the forces of inflation.  At 2% per year in inflation today's $1 will be worth about $0.55 in 30 years.
Based on your numbers, it sounds like you've got 12 years left in the private student loan, which just seems to be an annoyance to me.  You have the cash to pay it off, but that may not be the optimal solution. You've got $85k in cash!  That's way too much. So your options are:  -Invest 40k -Pay 2.25% loan off -Prepay mortgage 40k Play around with this link: mortgage calculator Paying the student loan, and applying the $315 to the monthly mortgage reduces your mortgage by 8 years. It also reduces the nag factor of the student loan. Prepaying the mortgage (one time) reduces it by 6 years. (But, that reduces the total cost of the mortgage over it's lifetime the most) Prepaying the mortgage and re-amortizing it over thirty years (at the same rate) reduces your mortgage payment by $210, which you could apply to the student loan, but you'd need to come up with an extra $105 a month.
"This is the meat of your potato question. The rephrasing of the question to a lending/real estate executive such as myself, I'd ask, what's the scenario? ""I would say you're looking for an Owner Occupied, Super Jumbo Loan with 20% Down or $360K down on the purchase price, $1.8 mil purchase price, Loan Amount is ~$1.45 mil. Fico is strong (assumption). If this is your scenario, please see image. Yellow is important, more debt increases your backend-DTI which is not good for the deal. As long as it's less than 35%, you're okay.  Can someone do this loan, the short answer is yes. It's smart that you want to keep more cash on hand. Which is understandable, if the price of the property declines, you've lost your shirt and your down payment, then it will take close to 10 years to recover your down. Consider that you are buying at a peak in real estate prices. Prices can't go up more than they are now. Consider that properties peaked in 2006, cooled in 2007, and crashed in 2008. Properties declined for more than 25-45% in 2008; regardless of your reasons of not wanting to come to the full 40% down, it's a bit smarter to hold on to cash for other investments purposes. Just incase a recession does hit.  In the end, if you do the deal-You'll pay more in points, a higher rate compared to the 40% down scenario, the origination fee would increase slightly but you'll keep your money on hand to invest elsewhere, perhaps some units that can help with the cashflow of your home. I've highlighted in yellow what the most important factors that will be affected on a lower down payment. If your debt is low or zero, and income is as high as the scenario, with a fico score of at least 680, you can do the deal all day long. These deals are not uncommon in today's market. Rate will vary. Don't pay attention to the rate, the rate will fluctuate based on many variables, but it's a high figure to give you an idea on total cost and monthly payment for qualification purposes, also to look at the DTI requirement for cash/debt.  See Image below:"
You can pretty much answer the question ""is it reasonable to retire right now?"" or ""could I retire in 5 years?"" (though with a retirement that could last 30 years, plenty of unknowns will remain even then). I think at age 20 or 30 though, just saving 15% (20% if you're conservative), and not spending too much time on a speculative analysis would be a sound decision. That's why I like the rule of thumb. Analysis paralysis (saving nothing or near-nothing) is the real danger early in one's career. Any plausible percentage is fine as long as you save. As your life unfolds and you see what happens, you can refine and correct, adjusting your savings rate, moving your retirement age around, spending a little less or more. The important thing earlier in life is to just get in the right ballpark."
"Understand your own risk tolerance and discipline. From Moneychimp we can see different market results - This is a 15 year span, containing what was arguably one of the most awful decades going. A full 10 year period with a negative return. Yet, the 15 year return was a 6.65% CAGR. You'd net 5.65% after long term cap gains. Your mortgage is likely costing ~4% or 3% after tax (This is not applicable to my Canadian friends, I understand you don't deduct interest). In my not so humble opinion, I'd pay off the highest rate debts first (unlike The David followers who are happy to pay off tens of thousands of dollars in 0% interest debt before the large 18% debt) and invest at the highest rate I'd get long term. The problem is knowing when to flip from one to the other. Here's food for thought - The David insists on his use of the 12% long term market return. The last 100 years have had an average 11.96% return, but you can't spend average, the CAGR, the real compound rate was 10.06%. Why would he recommend paying off a sub 3% loan while using 12% for his long term planning (All my David remarks are not applicable to Canadian members, you all probably know better than to listen to US entertainers)? I am retired, and put my money where my mouth is. The $200K I still owe on my mortgage is offset by over $400K in my 401(k). The money went in at 25%/28% pretax, has grown over these past 20 years, and comes out at 15% to pay my mortgage each month. No regrets. Anyone starting out now, and taking a 30 year mortgage, but putting the delta to a 15 year mortgage payment into their 401(k) is nearly certain to have far more in the retirement account 15 years hence than their remaining balance on the loan, even after taxes are considered. Even more if this money helps them to get the full matching, which too many miss. All that said, keep in mind, the market is likely to see a correction or two in the next 15 years, one of which may be painful.
My figuring (and I'm not an expert here, but I think this is basic math) is: Let's say you had a windfall of $1000 extra dollars today that you could either: a. Use to pay down your mortgage b. Put into some kind of equity mutual fund Maybe you have 20 years left on your mortgage.  So your return on investment with choice A is whatever your mortgage interest rate is, compounded monthly or daily.  Interest rates are low now, but who knows what they'll be in the future.  On the other hand, you should get more return out of an equity mutual fund investment, so I'd say B is your better choice, except: But that's also the other reason why I favour B over A.  Let's say you lose your job a year from now.  Your bank won't be too lenient with you paying your mortgage, even if you paid it off quicker than originally agreed.  But if that money is in mutual funds, you have access to it, and it buys you time when you really need it.  People might say that you can always get a second mortgage to get the equity out of it, but try getting a second mortgage when you've just lost your job.
Without commenting on whether or not it's needed I don't think we are going to see a QE3 and all the political pressure is for some reason to start raising rates.  Regardless of how it plays out it's safe to say that the Fed Rate isn't going any lower.   You should also watch closely what happens to Fannie and Freddie.  If they are dismantled and government backed mortgages become a thing of the past then I think it'll become impossible for a consumer to find a 30 year fixed rate mortgage.  Even if they are kept alive, they will be put on a short leash and that will serve to further depress the mortgage market. Long story short, I'd lock your rate in.
Even post meltdown, there are banks that will lend money based on a low loan to value, so 50% might not be a problem. But such loans come at a price. The current 30 year fixed rated is 4.5% or so, but you might see quite a bit higher than this on the loan.
"I'll add 2 observations regarding current answers. Jack nailed it - a 401(k) match beats all. But choose the right flavor account. You are currently in the 15% bracket (i.e. your marginal tax rate, the rate paid on the last taxed $100, and next taxed $100.) You should focus on Roth. Roth 401(k) (and if any company match, that goes into a traditional pretax 401(k). But if they permit conversions to the Roth side, do it) You have a long time before retirement to earn your way into the next tax bracket, 25%. As your income rises, use the deductible IRA/ 401(k) to take out money pretax that would otherwise be taxed at 25%. One day, you'll be so far into the 25% bracket, you'll benefit by 100% traditional. But why waste the opportunity to deposit to Roth money that's taxed at just 15%? To clarify the above, this is the single rate table for 2015: For this discussion, I am talking taxable income, the line on the tax return designating this number. If that line is $37,450 or less, you are in the 15% bracket and I recommend Roth. Say it's $40,000. In hindsight on should put $2,550 in a pretax account (Traditional 401(k) or IRA) to bring it down to the $37,450. In other words, try to keep the 15% bracket full, but not push into 25%. Last, after enough raises, say you at $60,000 taxable. That, to me is ""far into the 25% bracket."" $20,000 or 1/3 of income into the 401(k) and IRA and you're still in the 25% bracket. One can plan to a point, and then use the IRA flavors to get it dead on in April of the following year. To Ben's point regarding paying off the Student Loan faster - A $33K income for a single person, about to have the new expense of rent, is not a huge income.
I think the logic in your example demonstrates it is silly to make a decision for tax benefits alone.   Saving 75 is much preferred to a cash outflow of 100 less tax savings of 25. To answer your question, paying mortgage interest represents the fee for the cheapest money most people will ever access, which in itself is a benefit (e.g. renting vs buying). The benefits are maximized when the aggregate of  appreciation, inflation, tax savings exceeds total interest expense.
If it were me, I'd be debt free today, Monday, at latest.  100K-(53K+31.2K) = 15.8K would be my bank balance by this afternoon. I am not sure why you would count 6K of your daughter's money as yours to use.  Either it is her money, or yours, not both. If you still want debt, which I think is silly, you might try to refi your home with a home equity loan.  That loan would be in first position, at a fixed rate, and for a fixed term.  Regions bank did some thing like this for a person with excellent credit and plenty of equity.  They got a 7 year loan at 2.6% when the prevailing interest rate on a 15 year was about a point higher.
Congratulations on your bonus may many more come your way. I am having a bit of trouble following your numbers but it seems you are considering PMI for the life of your loan.  Once you get below 20% loan to value, you can petition the mortgage company to remove the PMI (with conventional loans; VA and FHA have lifetime PMI). If it was me, I'd do one of two things.  Both involve paying off the student loan now.  The savings from the student loan payment will assist you in helping you meet one of the two goals below.  Also both involve getting a 15 year fixed. The first would be to buy the house now, and work like crazy to get rid of the PMI.  My goal would be to get rid of this within 18 months.   The second would be to save up enough cash for the 20% down and then buy the house.  You'd miss out on the house you are looking at, which is kind of heartbreaking.  Who is to say that a better home does not come along at the same price?  My goal would be to have the downpayment in 9 months, and really try to have it in 6 months. Being an old guy that has experience how much of a virtue patience is, I'd recommend the second option.