Payment, the question is how many months will it take until the mortgage is Of payments, R = monthly payment, and D = debt balance after K payments, thenĭ = P × (1 + r) k - R × Ĭomponents: Suppose one decides to pay more than the monthly = principal, r = interest rate per period, n = number of periods, k = number Mortgage Payments Components: Let where P Makes the CD paying 9.8% compounded monthly really pay 10.25% interest over Thus, we get an effective interest rate of 10.25%, since the compounding Rate of r nom = 0.098, and an effective rate of: Numerical Example: A CD paying 9.8% compounded monthly has a nominal In this context r is also called the nominal rate, and This is the interest rate that would give the same yield if compounded only Invested at an annual rate r, compounded m times per year, the effective Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -Ĭonsiderably more than the corresponding simple interest. Year, with interest re-invested each month, the future value is Numerical Example: For 4-year investment of $20,000 earning 8.5% per One may solve for the present value PV to obtain: Where i = r/m is the interest per compounding period and n = mt is the Rate of r compounded m times per year for a period of t years is: Of an investment of present value (PV) dollars earning interest at an annual
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