Question

You want to have $100,000 to pay for one year of living expenses after you retire. You already have some money saved up, so you won’t need this money until long after you retire. You plan to have it invested for 50 years. However, you don’t know how much risk you’re willing to take on the investment. You are debating between two investments: Investment 1: An S&P 500 index fund, which has averaged 8.6% annual return since World War II Investment 2: Invests 90% in the S&P 500 index and 10% in US Treasuries, and has achieved an average 8.1% annual return since World War II.

a) How much do you need to invest now if you choose investment 1?

b) How much do you need to invest now if you choose investment 2?

Answer 1

We are reqiured to find the preaent value (PV)

a) How much do you need to invest now if you choose investment 1?

answer -

from the question we have the following inputs : FV is $100000, n = 50 years, Rate of interest (r) = 8.6%

PV = FV/ (1 + r)ⁿ = 100000/ (1 + 0.086)⁵⁰   = 100000/61.8716 = 1616.25

Hence, you need to invest $1616.25 now if you choose investment 1

b) How much do you need to invest now if you choose investment 2?

Answer -

rom the question we have the following inputs : FV is $100000, n = 50 years, Rate of interest (r) = 8.1%

PV = FV/ (1 + r)ⁿ = 100000/ (1 + 0.081)⁵⁰   = 100000/49.1230 = 2035.7063

Hence, you need to invest $2035.7063 now if you choose investment 2