Question

A woman buys an investment that pays 6% compounded semiannually. She wants $45,000 when she retires in 15 years. How much should she invest? the present value.) (Round your final answer to two decimal places.)

Answer 1

In order to determine how much is the amount the woman should invest, use the following formula for the amount of money earnt with compound interest:

`A=P(1+(r)/(n))^(nt)`

where,

A: amount obtained after t years = $45,000

P: principal investment = ?

r: percentage rate = 6% = 0.036

n: times at year = 2 (semiannually)

t: time = 15 years

Replace the previous values of the parameters and then solve for P, as follow:

`\begin{gathered} 45,000=P(1+(0.06)/(2))^(2\cdot15) \\ 45,000=P(2.43) \\ P=(45,000)/(2.43)=18,539.40 \end{gathered}`

Hence, the woman should invest approximately $18,539.40