You plan to retire at age 40 after a highly successful but short career. You wou

Question

You plan to retire at age 40 after a highly successful but short career. You would like to accumulate enough money by age 40 to withdraw $237,000 per year for 40 years. You plan to pay into your account 15 equal installments beginning when you are 25 and ending when you are 39. Your account bears interest of 10 percent per year.

1. How much do you need to accumulate in your account by the time you retire? (Round your final answer to the nearest dollar amount.)

2. How much do you need to pay into your account in each of the 15 equal installments? (Round your final answer to 2 decimal places.)

Explanation / Answer

Amount Required = Yearly Requirement * [ 1 - (1+r)-n ] / r

= $ 237,000 * [ 1 - (1+0.10)-40 ] / 0.10

= $ 237,000 * [ 1 - (1.10)-40 ] / 0.10

= $ 237,000 * [ 1 - 0.0221] / 0.10

= $ 237,000 * [ 0.9779 ] / 0.10

= $ 2,317,635

Amount Required in Account at the end of 40 Years is $ 2,317635 to give annual payment of $ 237,000 per anum for next 40 years.

Amount to be accumulated by 39 Years = 2317635 / 1.1

= $ 2,106,941

FV of ANnuity = Cash Flow * [ (1+r)n - 1 ] /r

$ 2,106,941 = Cash Flow * [ (1+0.10)15 - 1 ] / 0.10

$ 2,106,941 = Cash Flow * [ (1.10)15 - 1 ] / 0.10

$ 2,106,941 = Cash Flow * [ 4.1772 - 1 ] / 0.10

$ 2,106,941 = Cash Flow * [ 3.1772] / 0.10

Cash Flow = 2106941 * 0.10 / 3.1772

= 66313.39

Pls comment, if any further assistance is required.

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