Question

Find the future values of these ordinary annuities:

$700 per year for 9 years at 14% = $2,276.3640

$500 per year for 5 years at 6%= $669.1128

$250 per year for 4 years at 0%= $250

Rework a, b, and c for annuities due instead. How are the results different and why?

Answer 1

Considering Ordinary Annuity:

$700 per year for 9 years at 14%:

Future Value = $700*1.14^8 + $700*1.14^7 + ... + $700
Future Value = $700 * (1.14^9 - 1) / 0.14
Future Value = $11,259.7426

$500 per year for 5 years at 6%:

Future Value = $500*1.06^4 + $500*1.06^3 + ... + $500
Future Value = $500 * (1.06^5 - 1) / 0.06
Future Value = $2,818.5465

$250 per year for 4 years at 0%:

Future Value = $250 + $250 + $250 + $250
Future Value = $250 * 4
Future Value = $1,000

Considering Annuity Due:

$700 per year for 9 years at 14%:

Future Value = $700*1.14^9 + $700*1.14^8 + ... + $700*1.14
Future Value = $700 * 1.14 * (1.14^9 - 1) / 0.14
Future Value = $12,836.1066

$500 per year for 5 years at 6%:

Future Value = $500*1.06^5 + $500*1.06^4 + ... + $500*1.06
Future Value = $500 * 1.06 * (1.06^5 - 1) / 0.06
Future Value = $2,987.6593

$250 per year for 4 years at 0%:

Future Value = $250 + $250 + $250 + $250
Future Value = $250 * 4
Future Value = $1,000

Difference results from additional interest period for annuity due.