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

P=24.92 per quarter

Step-by-step 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*((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*((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*((1+(0.12/4))^(60*4)-1 )/((0.12/4))`

solving P

P=24.92