Question

If we place $8,592.00 in a savings account paying 7.5 percent interest compounded annually, how much will our account accrue to in 9.5 years?

Answer 1

Compound Interest Formula is:A = P * ( 1 + r )^nP = $8,592r = 7.5 % = 0.075n = 9.5 ( years )A = 8,592 * ( 1 + 0.075 )^(9.5)A = 8,592 * (1.075)^(9.5)A = 8,592 * 1.9878A = $17,079.48Answer: In 9.5 years there will be $17,079.48 on account.

Answer 2

$17,079.48.

Further explanation

Given:

• We place $8,592.00 in a savings account.
• Interest rate = 7.5% compounded annually (therefore 7.5% equal to 0.075).

Question:

How much will our account accrue to in 9.5 years?

The Process:

Compound interest is the interest earned from the initial amount and the interest earned previously. The formula for the balance A of the loan with compound interest is  

$\boxed{ \ A = P(1 + \frac{r}{n})^{nt} \ }$

• P = principal (initial amount)
• r = annual interest rate (in decimal form)
• t = time (in years)
• n = the number of periods of interest is compounded per year

For interest compounded annually, we can substitute 1 for n in the formula.

Let us calculate how much will our account accrue to in 9.5 years.

$\boxed{ \ A = 8,592(1 + 0.075)^{9.5} \ }$

$\boxed{ \ A = 8,592(1.075)^{9.5} \ }$

$\boxed{ \ A = 8,592 \times 1.987835 \ }$

$\boxed{ \ A = 17,079.47832 \ } \rightarrow \boxed{ \ A \approx 17,079.48 \ }$

Thus, the total amount of our account accrue to in 9.5 years is $17,079.48.

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Notes

What if the interest rate of 7.5% is compounded monthly (n = 12)?

$\boxed{ \ A = 8,592(1 + \frac{0.075}{12})^{12 \times 9.5} \ }$

$\boxed{ \ A = 8,592(1.00625)^{114} \ }$

$\boxed{ \ A = 8,592 \times 2.034566 \ }$

$\boxed{ \ A = 17,480.99107 \ } \rightarrow \boxed{ \ A \approx 17,480.99 \ }$

$\boxed{\boxed{ \ A = \ 17,480.99 \ }}$

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