Question

Jane is saving for her retirement. She just turned 27 and plans to retire when she is 65. She wants to have $3 million when she retires. The nominal annual interest rate is 4% compounded semi-annually. (All answers to 2 decimal places. Keep at least 5 decimal places for intermediate calculations.) Show your work

a) How much will she have to save every six months if she starts saving today? (Assume her final payment is six months before she turns 65).

b) How much will she have to save every six months if she doesn't start saving until 3 years from today?  

c) If the interest rate were 6%, how much would she have to save every six months if she starts saving today? (Assume her final payment is six months before she turns 65.)

Answer 1

Desired future amount = $3 million

a) Investment Life = 38 years

Annual Interest rate = 4% where semi annul interest rate would be 2%

Interest rate being compounded semi annually

3,000,000 = Payment * {[(1 + 0.02)^³⁸ - 1] / 0.02}

Payment semi annual would be 53,461.69

b) Investment Life = 35 years

Annual Interest rate = 4% where semi annul interest rate would be 2%

Interest rate being compounded semi annually

3,000,000 = Payment * {[(1 + 0.02)^³⁵ - 1] / 0.02}

Payment semi annual would be 60,006.62

c) Interest rate = 6% where semi annul interest rate would be 3%

Investment Life = 38 years

Interest rate being compounded semi annually

3,000,000 = Payment * {[(1 + 0.03)^³⁸ - 1] / 0.03}

Payment semi annual would be 43,378.02