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?

Explanation:

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

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