a. $22,332.96 will be in the account in 10 years
b. $22,362.49 will be in the account in 10 years
Step-by-step explanation:
The formula for compound interest, including principal sum is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per unit t
- t is the time the money is invested or borrowed for
∵ Angela invested $15,000 in a savings account
∴ P = 15,000
∵ The interest rate is 4%
∴ r = 4% = 4 ÷ 100 = 0.04
∵ The invested money will be in the account for 10 years
∴ t = 10
a. Compounded quarterly
∵ The interest is compound quarterly
∴ n = 4
- Substitute the values in the formula above
∵ [tex]A=15000(1+\frac{0.04}{4})^{(4)(10)}[/tex]
∴ [tex]A=15000(1+0.01)^{40}[/tex]
∴ [tex]A=15000(1.01)^{40}[/tex]
∴ A = 22332.96
$22,332.96 will be in the account in 10 years
b. Compounded monthly
∵ The interest is compound monthly
∴ n = 12
- Substitute the values in the formula above
∵ [tex]A=15000(1+\frac{0.04}{12})^{(12)(10)}[/tex]
∴ [tex]A=15000(1+\frac{1}{300})^{120}[/tex]
∴ A = 22362.49
$22,362.49 will be in the account in 10 years
Learn more:
You can learn more about the compounded interest in brainly.com/question/4361464
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