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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?

Respuesta :

Answer:

4.5%

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

[tex]\textup{Present value}=Amount invested\times(1+\frac{i}{100})^n[/tex]

on substituting the values, we get

[tex]\textup{76,662.25}=61,293\times(1+\frac{i}{100})^20[/tex]

or

( 1 + 0.01 × i )²⁰ = 1.250

or

or i = 1.122

thus,

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

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