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

(a) r = 5.25%,quarterly compounding

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(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(0.0525)/(4)\bigg)^(4)\\\\A = \$5,267.71`

b) r = 5%,monthly compounding

`A = 5000\bigg(1 + \displaystyle(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