Answer:
A. $22688.85
B. $22758.33
C. $22805.54
D. $22829.42
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
P = principal amount,
r = annual rate,
n = number of compounding periods,
t = number of years,
A. P = 15,000, t = 7, n = 2 ( semiannual ), r = 6% = 0.06,
Thus, the amount would be,
[tex]A=15000(1+\frac{0.06}{2})^{14}[/tex]
[tex]=15000(1+0.03)^{14}[/tex]
[tex]=15000(1.03)^{14}[/tex]
≈ $ 22688.85,
B. P = 15,000, t = 7, n = 4 ( quarters ), r = 6% = 0.06,
Thus, the amount would be,
[tex]A=15000(1+\frac{0.06}{4})^{28}[/tex]
≈ $ 22758.33,
C. P = 15,000, t = 7, n = 12 ( months ), r = 6% = 0.06,
Thus, the amount would be,
[tex]A=15000(1+\frac{0.06}{12})^{84}[/tex]
≈ $ 22805.54,
D. Now, the amount formula in compound continuously,
[tex]A=Pe^{rt}[/tex]
Where,
P = principal amount, r = annual interest, t = number of years,
Thus, the amount would be,
[tex]A=15000 e^{0.06\times 7}=15000 e^{0.42}\approx \$ 22829.42[/tex]
