The interest earned is $9,784.26 ⇒ 1st answer
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
The interest I = A - P
∵ The investment amount is $12,000
∴ P = 12,000
∵ The time of investment is 12 years
∴ t = 12
∵ The rate is 5% annual compounded quarterly
∴ r = 5% = 5 ÷ 100 = 0.05
∴ n = 4 ⇒ compounded quarterly
- Substitute these values in the rule above to find A
∴ [tex]A=12000(1+\frac{0.05}{4})^{(4)(12)}[/tex]
∴ [tex]A=12000(1+0.0125)^{48}[/tex]
∴ [tex]A=12000(1.0125)^{48}[/tex]
∴ A = 21,784.26
Subtract P from A to find the interest I
∵ P = 12,000
∵ A = 21,784.26
∴ I = 21,784.26 - 12,000
∴ I = 9784.26
The interest earned is $9,784.26
Learn more:
You can learn more about the compounded interest in brainly.com/question/4361464
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