Question

Angela invested $15,000 in a savings account. If the interest rate is 4%, how much will be in the account in 10 years by each method of compounding? Round your answers to the nearest cent.
a. compound quarterly
b. compound monthly

Answer 1

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

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

∵ $A=15000(1+\frac{0.04}{4})^{(4)(10)}$

∴ $A=15000(1+0.01)^{40}$

∴ $A=15000(1.01)^{40}$

∴ 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

∵ $A=15000(1+\frac{0.04}{12})^{(12)(10)}$

∴ $A=15000(1+\frac{1}{300})^{120}$

∴ 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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