Miss Elizabeth will be 25 years old tomorrow. She will receive the proceeds of a trust...

Miss Elizabeth will be 25 years old tomorrow. She will receive the proceeds of a trust fund that was set up by her wealthy grandmother. Her grandmother invested $10000at 5% when Elizabeth was 5 years old. Elizabeth plans to invest her inheritance with an insurance company at a guaranteed rate of 12% until she retires on her 55th birthday.

Elizabeth will also receive $5000 on her 25th birthday. This was the total prize money she won in a contest. She wishes to invest this at a Money Market fund with an expected return of 5.25% until she retires.

At retirement, Elizabeth will begin to draw down her investment in 30 equal installments calculated to reduce her investments fund to $0. She will make each withdrawal at the end of the year and that the money that remains reinvested will continue to earn 10%.

What will be the amount of each installment?

Solutions

Expert Solution

Total money available to Elizabeth at the time of retirement = Future value of money invested with insurance company + Future value of money invested in money market fund

When Elizabeth was 5 years old, her grandmother invested $10000 at 5%, and the value of this amount when she is 25 years old = $ 10000 ( 1 + 0.05 ) ²⁰ = $ 26532.97 $ 26533

Future value of money invested with insurance company which is the money obtained as inheritance = $ 26533 ( 1 + 0.12 )³⁰

Future value of money invested with insurance company = $ 794,926.6 $ 794,927

Future value of money invested in money market fund which is also the prize money = $ 5000 ( 1 + 0.0525 )³⁰ = $ 23207.8 $ 23208

The amount available to Elizabeth at the time of retirement = $ 794,927 + $ 23208 = $ 817505

The amount of each installment is found using present value of annuity method.

The amount of each installment = $ 86720.3

jeff jeffy answered 1 year ago

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