You deposit $2,600 at the beginning of every year for 30 years into an investment that earns 9.5%. At the end of 30 years you put the investment into an account that earns 3.5%. This account will be used to fund a 25-year annuity. If you take the money out at the end of every year, what is the annual annuity amount you will withdraw yearly for 25 years?

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Business

Trace Wagner

7 September, 13:45

You deposit $2,600 at the beginning of every year for 30 years into an investment that earns 9.5%. At the end of 30 years you put the investment into an account that earns 3.5%. This account will be used to fund a 25-year annuity. If you take the money out at the end of every year, what is the annual annuity amount you will withdraw yearly for 25 years?

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Brooke Aguirre · Answer 1

First, find the future value of the deposits at the end of 30 years. They are in the form of an Annuity Due, therefore, set your financial calculator to BGN mode;

Total duration; N = 30

One-time present cashflow; PV = 0

Interest rate per year; I/Y = 9.5%

Recurring payment; PMT = - 2,600

then CPT FV = 426,160.32

Next, find the recurring amount of withdrawal for the 25 years. Because this is an ordinary annuity (made at the end of every year), set your financial calculator back to "END" mode;

Total duration; N = 25

Present value; PV = - 426,160.32

Interest rate per year; I/Y = 3.5%

One-time future cashflow FV = 0

then CPT PMT = 25,856.87

Therefore annual annuity amount you will withdraw is $25,856.87