Question

A person wants to have $25,000 cash for a new car 5 years from now. how much should be placed in an account now if the account pays 4.75% compounded weekly? compute the answer to the nearest dollar.

Answer 1

Given

Future value of an investment at 4.75% compounded weekly is $25,000

Find

The present value of the investment, to the nearest dollar

Solution

The multiplier is (1 + .0475/52)^(52·5) ≈ 1.2679375, so the amount required is found from

... 1.2679375×present value = 25,000

... present value = 25,000/1.2679375 ≈ 19,717

$19,717 needs to be placed in the account now.

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When an annual interest rate r is compounded n times per year, the annual multiplier is (1 +r/n)^n. Here, we have n=52 (weeks per year). The multiplier is applied 5 times (raised to the 5th power) to obtain the result of a 5-year investment.