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Anuta_ua [19.1K]
3 years ago
5

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?
Mathematics
2 answers:
Reika [66]3 years ago
7 0
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.

Hunter-Best [27]3 years ago
3 0

$17,079.48.

<h3>Further explanation</h3>

<u>Given:</u>

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

<u>Question:</u>

How much will our account accrue to in 9.5 years?

<u>The Process:</u>

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.

- - - - - - -

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 \ }}

<h3>Learn more</h3>
  1. Melanie is looking for a loan brainly.com/question/2708838
  2. How much money did Jenny earn in all brainly.com/question/2068148#
  3. What is the total amount owed at the end of the 4 years? brainly.com/question/13675435
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