Question

A person establishes a sinking fund for retirement by contributing $5,000 per year at the end of each year for 5 years. For the next 10 years, equal yearly payments are withdrawn, at the end of which time the account will have a zero balance. If money is worth 4% compounded annually, what yearly payments will the person receive for the last 10 years?

Answer 1

Contribution per year = $5000

Investment period = 5 years

Interest rate = 4%

The future value of these contributions at the end of 5 years can be calculated using FV function in spreadsheet

FV(rate, number of periods, payment amount, present value, when-due)

Where, rate = annual interest rate = 4%

number of periods = 5 years

payment amount = Contribution per year = $5000

present value = present value of investments = 0

when-due = when is the contribution made each year = end = 0

The future value of contributions at the end of 5 years = FV(4%, 5, -5000, 0, 0) = $27,081.6128

The payment received at the end of each year for 10 years can be calculated using PMT function in spreadsheet

PMT(rate, number of periods, present value, future value, when-due)

Where, rate = annual interest rate = 4%

number of periods = 10 years

present value = value of contributions at the end of 5 years = $27,081.6128

future value = 0

when-due = when is the withdrawal made each year = end = 0

The payment received at the end of each year for 10 years = PMT(4%, 10, 27081.6128, 0, 0) = $3,338.9176