Question

The APR of Kylee's savings account is 5.6%, and interest is compounded quarterly. If the principal in Kylee's savings account was $5800 for an entire year, what will be the balance of her account after all the interest is paid for the year? Show your work.

Answer 1

Using the attached formula:
Total = 5,800 * (1 + (.056/4))^4*1
Total = 5,800 * (1.014)^4
Total = 5,800 * 1.0571870144
Total = 6,131.6846836128
Total = 6,131.68

Answer 2

The balance of Kylee's account after all the interest is paid for the year is $6131.76.

Explanation:

Formula for compounded quarterly

`Amount = P(1 + (r)/(4))^(4t)`

Where P is the principle , r is the rate of interest in the decimal form and t is the time in years.

As given

The APR of Kylee's savings account is 5.6%, and interest is compounded quarterly. If the principal in Kylee's savings account was $5800 for an entire year.

Here

P = $5800

5.6 % is written in the decimal form.

`= (5.6)/(100)`

= 0.056

r = 0.056

t = 1 year

put in the formula

`Amount = 5800(1 + (0.056)/(4))^(4)`

`Amount = 5800(1 + 0.014)^(4)`

`Amount = 5800(1.014)^(4)`

`Amount = 5800* 1.0572\ (Approx)`

Amount = $6131.76

Therefore the balance of Kylee's account after all the interest is paid for the year is $6131.76.