Question

# How much money must you deposit into a savings account at the end of each year...

How much money must you deposit into a savings account at the end of each year at 4% interest compounded annually in order to earn \$9,778.08 interest during a 20-year period?

Amount = Principal * (1+ rate)time period

[Principal + interest] = Principal * (1+ rate)time period

[Principal + 9778.08 ] = Principal * (1+ 0.04)20

[Principal + 9778.08 ] = Principal * (1.04)20

Principal + 9778.08 = 2.191123 principal

9778.08 = 1.191123 principal

Principle = 9778.08 / 1.191123

Principal = 8209.13

Future value of ordinary annuity = payment* [(1+rate)number of payments - 1] / rate

17987.21 = payments* [(1+0.04)20 - 1] / 0.04

17987.21 = payments* [(1.04)20 - 1] / 0.04

17987.21 = payments* [2.191123 - 1] / 0.04

719.49 = payments* [2.191123 - 1]

719.4884 = payments* 1.191123

\$604.04 = payments

money must be deposited into a savings account at the end of each year = \$604.04

Note:-  Future value = 8209.13 + 9778.08

= \$17987.21