Question

Diana invested $61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had $76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account?

Answer 1

4.5%

Step-by-step explanation:

Given:

Amount invested = $61,293

Time period = 5 years

Interest is compounded quarterly , thus, n = 5 × 4 = 20

Final amount = $76,662.25

Let the interest rate be 'i%' quarterly

Now,

for compound interest

`\textup{Present value}=Amount invested*(1+(i)/(100))^n`

on substituting the values, we get

`\textup{76,662.25}=61,293*(1+(i)/(100))^20`

or

( 1 + 0.01 × i )²⁰ = 1.250

or

or i = 1.122

thus,

annual interest rate = 1.122 × 4 = 4.488 ≈ 4.5%