Question

A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying 12% compounded quarterly at the time of your birth to yield $1,000,000 when you retire at age 60? (Round your answer to the nearest cent.)

Answer 1

Answer:

P=24.92 per quarter

Explanation:

this problem can be solved applying the concept of annuity, keep in mind that an annuity is a formula which allows you to calculate the future value of future payments affected by an interest rate.by definition the future value of an annuity is given by:

$s_{n} =P*\frac{(1+i)^{n}-1 }{i}$

where $s_{n}$ is the future value of the annuity, $i$ is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so applying to this particular problem, we have:

$s_{60*4} =P*\frac{(1+(0.12/4))^{60*4}-1 }{(0.12/4)}$

we will asume that deposits are made as interest is compounded it is quarterly thats why we multiply 60 and 4 and also we divide 12% into 4, so:

$1,000,000 =P*\frac{(1+(0.12/4))^{60*4}-1 }{(0.12/4)}$

solving P

P=24.92