Businesses must expect that the rate of return from buying the new capital will be greater than the interest rate they must pay to finance the new capital. At higher interest rates, fewer investments meet the expectations criteria. At lower interest rates, more investments meet the expectations criteria. Therefore, businesses will invest more when interest rates are low and less when interest rates are high. Saving is positively related to the interest rate.
Interest is the opportunity cost of foregone consumption by households.
When interest rates are higher, the opportunity cost of present consumption is greater, and when interest rates are lower, the opportunity cost of present consumption is much less. Higher interest rates are a greater inducement for households to forego current consumption, while lower interest rates are a greater inducement for households to spend. Therefore, households will save more when interest rates are higher and less when interest rates are lower. The equilibrium rate of interest is the rate of interest at which investment equals saving. At this rate the amount of saving made available by households is exactly the amount that businesses need for investment in new capital.