Question

Marcia Stubern is planning for her golden years. She will retire in 20 years, at which time she plants to begin withdrawing $50,000 annually to pay for living expenses. He is expected to live for 30 years following her retirement. Her financial advisor thinks she can earn 7% annually before retirement and 10% after his retirement. How much does he need to invest at the end of each quarter to prepare for his fnancial needs after retirement.

Answer 1

After retirement:

Annual Withdrawal = $50,000
Period = 30 years
Interest Rate = 10%

Amount required at retirement = $50,000 * PVIFA(10%, 30)
Amount required at retirement = $50,000 * (1 - (1/1.10)^30) / 0.10
Amount required at retirement = $471,345.72

Before retirement:

Amount required at retirement = $471,345.72
Annual Interest Rate = 7%
Quarterly Interest Rate = 1.75%
Period = 80 quarters or 20 years

Quarterly Payment * FVIFA(1.75%, 80) = $471,345.72
Quarterly Payment * (1.0175^80 - 1) / 0.0175 = $471,345.72
Quarterly Payment * 171.79384 = $471,345.72
Quarterly Payment = $2,743.67

So, Marcia needs to save $2,743.67 every quarter