Question

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?

Answer 1

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