7500 dollars is placed in an account with an annual interest rate of 7.75%. To the nearest year, how long will it take for the account value to reach 38200 dollars?

It will take 55 years for the account value to reach 38200 dollars

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

.

In this problem, we ahve that:

So

First we find how much we have to earn in interest.

.

How much time to earn this interest?

Rounding up

It will take 55 years for the account value to reach 38200 dollars