A baby's parents want to provide for college. How much should be deposited on each of the child's first 17

A baby's parents want to provide for college. How much should be deposited on each of the child's first 17 birthdays to be able to withdraw 20,000 on each of the next 4 birthdays? Assume an interest rate of 5%.

Solutions

Expert Solution

Calculation of amount required at 17th birthday;

Formula;

Amount required at 17th birthday = Annual withdraw * [1 - (1 + interest rate)^-withdrawal period] / Interest rate

Amount required at 17th birthday = 20,000 * [1 - (1 + 0.05)^-4] / 0.05

Amount required at 17th birthday = 400,000 * (1 - 1.05^-4)

Amount required at 17th birthday = 400,000 * (1 - 0.822702474791882)

Amount required at 17th birthday = 400,000 * 0.177297525208118

Amount required at 17th birthday = 70919.0100832472

Calculation of annual deposit required for 17 years;

Formula;

Amount required at 17th birthday = Annual Deposit * [(1 + interest rate)^deposit period - 1] / Interest rate

70919.0100832472 = Annual Deposit * [(1 + 0.05)^17 - 1] / 0.05

70919.0100832472 * 0.05 = Annual Deposit * (1.05^17 - 1)

3545.95050416236 = Annual Deposit * (2.29201831780103 - 1)

3545.95050416236 = Annual Deposit * 1.29201831780103

Annual deposit = 3545.95050416236 / 1.2920183178010

Annual deposit = 2,744.50482265409 or 2,744.50 (Approx.)

Annual deposit required for 17 years = 2,744.50 (Approx.)

Junaid answered 1 year ago

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