Question

In: Finance

You deposit $10,000 in a certificate of deposit that pays interest of 4.25% per annum. What...

You deposit $10,000 in a certificate of deposit that pays interest of 4.25% per annum.

What amount will your deposit grow to after five years if the bank compounds interest:

a. Annually

b. Semi-Annually

c. Quarterly

d. Monthly

e. Daily

Please show all your work and explain your answers.

 

Solutions

Expert Solution

Answer a.

Amount Invested = $10,000
Annual Interest Rate = 4.25%
Period = 5 years

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $10,000 * 1.0425^5
Future Value = $12,313.47

Answer b.

Amount Invested = $10,000
Annual Interest Rate = 4.25%
Semiannual Interest Rate = 2.125%
Semiannual Period = 10 (5 years)

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $10,000 * 1.02125^10
Future Value = $12,340.16

Answer c.

Amount Invested = $10,000
Annual Interest Rate = 4.25%
Quarterly Interest Rate = 1.0625%
Period = 5 years or 20 quarters

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $10,000 * 1.010625^20
Future Value = $12,353.81

Answer d.

Amount Invested = $10,000
Annual Interest Rate = 4.25%
Monthly Interest Rate = 0.354167%
Period = 5 years or 60 months

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $10,000 * 1.00354167^60
Future Value = $12,363.02

Answer e.

Amount Invested = $10,000
Annual Interest Rate = 4.25%
Daily Interest Rate = 0.01164%
Period = 5 years or 1,825 days

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $10,000 * 1.0001164^1,825
Future Value = $12,366.64


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