Question

You have just purchased a new home. No money was required as a down payment; you will be making payments of $2,000 per month (think of these as annual payments of $24,000) for the next 30 years. Determine the present value of your future payments at each of the following interest rates:

a. 2% b. 4% c. 6% d. 8%

Answer 1

Answer 2

To determine the present value of your future payments at each of the given interest rates, we can use the formula for calculating the present value of an ordinary annuity. The formula is:

Present Value = Payment Amount × [(1 - (1 + Interest Rate)^(-Number of Periods)) / Interest Rate]

where: Payment Amount = $24,000 (annual payment) Interest Rate = Annual interest rate (expressed as a decimal) Number of Periods = Total number of periods (years)

Let's calculate the present value at each interest rate:

a. 2%: Interest Rate = 0.02 Number of Periods = 30

Present Value = $24,000 × [(1 - (1 + 0.02)^(-30)) / 0.02] Present Value ≈ $453,407.85

b. 4%: Interest Rate = 0.04 Number of Periods = 30

Present Value = $24,000 × [(1 - (1 + 0.04)^(-30)) / 0.04] Present Value ≈ $386,938.97

c. 6%: Interest Rate = 0.06 Number of Periods = 30

Present Value = $24,000 × [(1 - (1 + 0.06)^(-30)) / 0.06] Present Value ≈ $331,644.57

d. 8%: Interest Rate = 0.08 Number of Periods = 30

Present Value = $24,000 × [(1 - (1 + 0.08)^(-30)) / 0.08] Present Value ≈ $284,316.86

So, the present value of your future payments at each interest rate would be approximately: a. $453,407.85 b. $386,938.97 c. $331,644.57 d. $284,316.86