Question

# You are responsible to pay back the following: \$400 due today, \$500 due in five months,...

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?

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

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