Question

Certificate of Deposit You want to invest $5000 in a certificate of deposit for 12 months.You are given the options below.which would you choose?Explain.
(a) r = 5.25%,quarterly compounding
(b) r = 5%,monthly compounding
(c) r = 4.75%,continuous compounding

Answer 1

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

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

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

$A = Pe^{rt}$

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

$A = 5000\bigg(1 + \displaystyle\frac{0.0525}{4}\bigg)^{4}\\\\A = \ 5,267.71$

b) r = 5%,monthly compounding

$A = 5000\bigg(1 + \displaystyle\frac{0.05}{12}\bigg)^{12}\\\\A = \ 5,255.80$

c)  r = 4.75%, Continuously compounding

$A = 5000e^{0.0475}\\A = \ 5,243.23$

Since, the maximum amount on the principal value is given by r = 5.25%,quarterly compounding