Jen opened a savings account and deposited as principal. The account earns
interest, compounded quarterly. What is the balance after 5 years?
Use the formula , where is the balance (final amount), is the principal
(starting amount), is the interest rate expressed as a decimal, is the number of times per
year that the interest is compounded, and is the time in years.
Round your answer to the nearest cent.

Ask by Turnbull Mccarthy. in the United States

Mar 24,2025

Question

Jen opened a savings account and deposited as principal. The account earns
interest, compounded quarterly. What is the balance after 5 years?
Use the formula , where is the balance (final amount), is the principal
(starting amount), is the interest rate expressed as a decimal, is the number of times per
year that the interest is compounded, and is the time in years.
Round your answer to the nearest cent.

Ask by Turnbull Mccarthy. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

To find the balance after 5 years in the savings account, we can use the formula for compound interest:

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

Given:
- Principal (P) = $1,229.00
- Interest rate (r) = 6% = 0.06 (as a decimal)
- Compounded quarterly, so n = 4
- Time (t) = 5 years

Substitute the given values into the formula:

$$ A = 1229.00\left(1 + \frac{0.06}{4}\right)^{4 \times 5} $$

Now, we can calculate the balance after 5 years using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$1229\left(1+\frac{0.06}{4}\right)^{4\times 5}$$
- step1: Divide the terms:
  $$1229\left(1+\frac{3}{200}\right)^{4\times 5}$$
- step2: Add the numbers:
  $$1229\left(\frac{203}{200}\right)^{4\times 5}$$
- step3: Multiply the numbers:
  $$1229\left(\frac{203}{200}\right)^{20}$$
- step4: Simplify:
  $$1229\times \frac{203^{20}}{200^{20}}$$
- step5: Multiply:
  $$\frac{1229\times 203^{20}}{200^{20}}$$
The balance after 5 years in the savings account is approximately $1,655.28.

Therefore, after 5 years, the balance in the savings account will be $1,655.28.
After 5 years, the balance in the savings account will be $1,655.28.

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