Question

Edwina wants to leave $5 million to her favorite charity when she dies. If Edwina plans to retire at 70 and live to age 100 and if she can earn 8% on her investments, what lump sum over and above what she needs to fund retirement will she need when she retires?

a.) $5,000,000
b.) $848,527
c.) $637,664
d.) $496,887

Answer 1

Edwina needs to have a lump sum of $496,887 when she retires at age 70 to ensure she can leave $5 million to her favorite charity at age 100, assuming an 8% annual interest rate.

Step-by-step explanation:

The question involves calculating the present value of a future sum of money when the investment earns a certain rate of interest. To determine what lump sum Edwina needs when she retires at age 70 to leave $5 million to her favorite charity at age 100, we can use the formula for the present value of a future amount: Present Value = Future Value / (1 + r)^n, where r is the annual interest rate (expressed as a decimal), and n is the number of years until the amount will be given to the charity.

Using this formula with a future value of $5,000,000, an annual interest rate of 8% (0.08), and 30 years (100 - 70), the calculation is:

Present Value = $5,000,000 / (1 + 0.08)^30

Present Value = $5,000,000 / (1.08)^30

Present Value = $5,000,000 / 10.06266

Present Value = $496,886.20 (rounded to the nearest dollar)

Therefore, the correct answer is d.) $496,887.