Question

You are responsible to pay back the following: $400 due today, $500 due in five months, and $618 due in one year. You are given the option: instead of making the above 3 payments, you can pay the same amount as a single payment 9 months from now. Assuming a 12% per annum (p.a) interest rate, how much will the single payment be?

Answer 1

present value = future value / (1 + interest rate)ⁿ, where n = time in years

future value = present value * (1 + interest rate)ⁿ, where n = time in years

Value of single payment = future value of $400 after 9 months + future value of $500 after 9 months + present value of $618 after 9 months

Value of single payment = ($400 * (1 + 12%)^9/12) + ($500 * (1 + 12%)^4/12) + ($618 / (1 + 12%)^3/12​​​​​​​)

Value of single payment = $435.49 + $519.25 + $600.74

Value of single payment = $1,555.47