Question

20. Assume that you are setting up your retirement plan by considering two investment plans together. (Your retirement in 20 years). You want to earn a total of $1,000,000 after 20 years from the following two investment plans together. Investment plan #1 : You currently have $20,000 in the bank and decide to invest that $20,000 in a money market account for 20 years which you feel will generate a return on 6% per year. Investment plan #2: You also intend on investing additional money at the end of each year for 20 years in a stock market mutual fund that you believe will return 10% per year. o o Question: in your investment plan #2, ifyou make 20 equal annual investments at the end of each year for 20 years into the stock market mutual fund, how much will you need to invest each year in order to have a total of $1,000,000 from both investment plans after 20 years? Total of $1,000.000 is the sum of your two investment outcomes after 20 years)

Answer 1

Investment Plan 1

FV of $ 20,000 in money market account with i = 6% over N = 20 years will be = 20,000 x (1 + i)^N = 20,000 x (1 + 6%)²⁰ = $  64,143

Investment plan 2

Let the annual amount be. It's thus an annuity of A at r = 10% over N = 20 years

Hence, FV of annuity = A / r x [(1 + r)^N - 1] = A / 10% x [(1 + 10%)²⁰ - 1] =  57.27A

Hence, FV of investment plan 1 + FV under investment plan 2 = 1,000,000

Hence, 64,143 + 57.27A = 1,000,000

Hence, A = $ 16,340 is the amount we need to invest annually.