Answer:
(a) r = 5.25%,quarterly compounding
Step-by-step explanation:
We are given the following in the question:
P = $5000
t = 12 months = 1 year
The compound interest is given by
[tex]A = P\bigg(1 + \displaystyle\frac{r}{n}\bigg)^{nt}[/tex]
where P is the principal, r is the interest rate, t is the time, n is the nature of compound interest and A is the final amount.
When compounded continuously
[tex]A = Pe^{rt}[/tex]
where P is the principal, r is the interest rate, t is the time and A is the final amount.
a) r = 5.25%,quarterly compounding
[tex]A = 5000\bigg(1 + \displaystyle\frac{0.0525}{4}\bigg)^{4}\\\\A = \$5,267.71[/tex]
b) r = 5%,monthly compounding
[tex]A = 5000\bigg(1 + \displaystyle\frac{0.05}{12}\bigg)^{12}\\\\A = \$5,255.80[/tex]
c) r = 4.75%, Continuously compounding
[tex]A = 5000e^{0.0475}\\A = \$5,243.23[/tex]
Since, the maximum amount on the principal value is given by r = 5.25%,quarterly compounding
