Question

$4000 is placed in an account with an annual interest rate of 7.25%. To the nearest tenth of a year, how long will it take for the account value to reach $28200?

a) 5.7 years
b) 6.1 years
c) 7.3 years
d) 8.6 years

Answer 1

Using the formula for compound interest, with the principal amount, interest rate, and desired final amount provided, the time required for the account to reach $28200 is approximately 7.3 years.

Step-by-step explanation:

To find out how long it will take for an account with $4000 at a 7.25% annual interest rate to grow to $28200, we use the formula for compound interest. We can use the formula A = P(1 + r/n)nt, where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

Since the interest is compounded annually, n = 1. The formula simplifies to A = P(1 + r)t. To find t, we rearrange the formula to solve for t, which gives us t = log(A/P) / log(1 + r).

Substituting the given values:

A = $28200
P = $4000
r = 7.25% = 0.0725

So we have t = log(28200/4000) / log(1 + 0.0725).

Calculating this, we get t ≈ 7.3 years.

Therefore, it will take approximately 7.3 years for the account value to reach $28200, so the correct answer is c) 7.3 years.