Question

A young couple, both 25 years old, are planning to retire in 40 years at the age of 65. After they retire,

they expect to live for an additional 20 years, until age 85. They plan to begin saving for retirement today

and based on information from their financial planner, they think they will earn 8% on their investment

compounded annually. They think they will earn 5% on their retirement savings after they retire.

If they begin at age 25 to save $5,000 per year for the next 40 years. Assume they will be selling

their business in 5 years for $100,000, which will be deposit into their retirement account and

leave there until age 65. How much will this couple have saved in their retirement account at age

65?

Answer _____________________ (10 points)

Answer 1

Annual contribution = $ 5000

Number of years (n) = 40

rate of interest (r) = 8%

Retirement Saving =  contribution*((1+r)ⁿ - 1)/ r

= $ 5000 * (1 + 0.08)⁴⁰ - 1 / 0.08

= $ 5000 * 259.0565

= $ 1295283

Proceed from sale of business in 5 years= $100000

Value of savings from sale of business = $ 100000 * (1+0.08)³⁵

= 1478534

Couple have saved in their retirement account at age 65 = $1295283 + 1478534 = 2,773,817