Question

1. Find the following values assuming a regular, or ordinary, annuity:

The present value of $400 per year for ten years at 10 percent

The future value of $400 per year for ten years at 10 percent

The present value of $200 per year for five years at 5 percent

The future value of $200 per year for five years at 5 percent

Answer 1

Answer a.

Annual Payment = $400
Interest Rate = 10%
Time Period = 10 years

Present Value = $400/1.10 + $400/1.10^2 + … + $400/1.10^9 + $400/1.10^10
Present Value = $400 * (1 - (1/1.10)^10) / 0.10
Present Value = $400 * 6.144567
Present Value = $2,457.83

Answer b.

Annual Payment = $400
Interest Rate = 10%
Time Period = 10 years

Future Value = $400*1.10^9 + $400*1.10^8 + … + $400*1.10 + $400
Future Value = $400 * (1.10^10 - 1) / 0.10
Future Value = $400 * 15.93742
Future Value = $6,374.97

Answer c.

Annual Payment = $200
Interest Rate = 5%
Time Period = 5 years

Present Value = $200/1.05 + $200/1.05^2 + $200/1.05^3 + $200/1.05^4 + $200/1.05^5
Present Value = $200 * (1 - (1/1.05)^5) / 0.05
Present Value = $200 * 4.32948
Present Value = $865.90

Answer d.

Annual Payment = $200
Interest Rate = 5%
Time Period = 5 years

Future Value = $200*1.05^4 + $200*1.05^3 + $200*1.05^2 + $200*1.05 + $200
Future Value = $200 * (1.05^5 - 1) / 0.05
Future Value = $200 * 5.52563
Future Value = $1,105.13