Find the amount to which 400 will grow under each of these c

Find the amount to which $400 will grow under each of these conditions:

12% compounded annually for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent

. $ 12% compounded semiannually for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

$ 12% compounded quarterly for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

$ 12% compounded monthly for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

$ 12% compounded daily for 6 years. Do not round intermediate calculations. Round your answer to the nearest cent.

$ Why does the observed pattern of FVs occur?

Solution

Answer a.

Amount Invested = $400
Annual Interest Rate = 12%
Period = 6 years

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $400 * 1.12^6
Future Value = $789.53

Answer b.

Amount Invested = $400
Annual Interest Rate = 12%
Semiannual Interest Rate = 6%
Semiannual Period = 12

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $400 * 1.06^12
Future Value = $804.88

Answer c.

Amount Invested = $400
Annual Interest Rate = 12%
Quarterly Interest Rate = 3%
Quarter Period = 24

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $400 * 1.03^24
Future Value = $813.12

Answer d.

Amount Invested = $400
Annual Interest Rate = 12%
Daily Interest Rate = 0.0329%
Period = 2,190

Future Value = Amount Invested * (1 + Interest Rate)^Period
Future Value = $400 * 1.000329^2,190
Future Value = $822.10

Answer e.

FV will increase with increase in number of compounding per year.