It is now January 1. You plan to invest a total of 5 consecutive, equal deposits, one every 6 months, with the first payment being made today. The account pays an interest rate of 6% (APR) but uses semiannual compounding. You plan to leave the money in the bank for 10 years. Your goal is to withdraw $25,000 in 10 years. To get the money for this withdrawal, you will make the aforementioned five equal deposits, beginning today and for the following 4 semiyears (6 month periods). How large must each of the five payments be

$2,848.94

Explanation:

first of all, we must determine the amount of money that we need to have in our account in order to be able to withdraw $25,000 in 10 years.

You will start making your semiannual deposits today and they will end in exactly 2 years, so we need to find out the present value of the $25,000 in two years:

PV = $25,000 / (1 + 3%)¹⁶ = $15,579.17

that is now the future value of our annuity due:

FV = semiannual deposit x FV annuity due factor (3%, 5 periods)

$15,579.17 = semiannual deposit x 5.46841

semiannual deposit = $15,579.17 / 5.46841 = $2,848.94

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