A student wants to save $8000 for college in five years. How much should be put every year into an account that earns 5.2 percent annual interest?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The student wants to have $8000 at the end of 5 years by placing a certain amount in an account every year where he is able to earn 5.2 interest annually.

Let the amount be X. The amount that is placed in year 1 increases to X*(1 + 5.2%)^5 after...

See
This Answer Now

Start your subscription to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your Subscription

The student wants to have $8000 at the end of 5 years by placing a certain amount in an account every year where he is able to earn 5.2 interest annually.

Let the amount be X. The amount that is placed in year 1 increases to X*(1 + 5.2%)^5 after 5 years and the amount placed in year 2 increases to X*(1 + 5.2%)^4. In the same way we can derive what the amount placed in the other years becomes.

At the end of year 5 he has $8000

X * [ (1.052)^5 +(1.052)^4 +(1.052)^3 +(1.052)^2 +(1.052)^1] = 8000

The series within the brackets is a GP, with the first term 1.052 and the common ratio 1.052. The sum of 5 such terms is 1.052*( 1.052^5 – 1) / ( 1.052 – 1)

=>1.052*( 1.052^5 – 1) / ( 0.052)

=> 5.836

X = 8000 / 5.836

=> $1370.8

The student should put $1370.80 into the account every year.

Approved by eNotes Editorial Team