Question

5-14 FUTURE VALUE OF AN ANNUITY Find the future values of these ordinary annuities. Compounding occurs once a year. a. $500 per year for 8 years at 14% b. $250 per year for 4 years at 7% c. $700 per year for 4 years at 0% d. Rework parts a, b, and c assuming they are annuities due.

Answer 1

Answer a.

Annual Payment = $500
Number of Payments = 8
Interest Rate = 14%

Future Value = $500*1.14^7 + $500*1.14^6 + … + $500*1.14 + $500
Future Value = $500 * (1.14^8 - 1) / 0.14
Future Value = $500 * 13.232760
Future Value = $6,616.38

Answer b.

Annual Payment = $250
Number of Payments = 4
Interest Rate = 7%

Future Value = $250*1.07^3 + $250*1.07^2 + $250*1.07 + $250
Future Value = $250 * (1.07^4 - 1) / 0.07
Future Value = $250 * 4.439943
Future Value = $1,109.99

Answer c.

Annual Payment = $700
Number of Payments = 4
Interest Rate = 0%

Future Value = $700 + $700 + $700 + $700
Future Value = $700 * 4
Future Value = $2,800

Answer d.

Annuity 1:

Annual Payment = $500
Number of Payments = 8
Interest Rate = 14%

Future Value = $500*1.14^8 + $500*1.14^7 + … + $500*1.14^2 + $500*1.14
Future Value = $500 * 1.14 * (1.14^8 - 1) / 0.14
Future Value = $500 * 15.085347
Future Value = $7,542.67

Annuity 2:

Annual Payment = $250
Number of Payments = 4
Interest Rate = 7%

Future Value = $250*1.07^4 + $250*1.07^3 + $250*1.07^2 + $250*1.07
Future Value = $250 * 1.07 * (1.07^4 - 1) / 0.07
Future Value = $250 * 4.750739
Future Value = $1,187.68

Annuity 3:

Annual Payment = $700
Number of Payments = 4
Interest Rate = 0%

Future Value = $700 + $700 + $700 + $700
Future Value = $700 * 4
Future Value = $2,800