Question

Suppose you have determined that you want to have retirement savings of $5,000,000 when you retire at age 65, 42 years after you graduate, at age 23. Looking at the long history of the market, you are confident that you can earn at 10% per annum on a well-diversified equity portfolio. Required: a) Calculate much would you have to save annually at the end of each year for the next 42 years to reach your $5,000,000 goal assuming a 10% annual rate of return? b) How much would you need to invest at age 23 to have $5,000,000 in your portfolio at age 65? c) To avoid carry-forward issues, we will assume that the answer in part (a) is $100,000. Suppose that at age 23, you borrow $100,000, paying interest at 4.5% APR, compounded monthly on a 10-year amortization. What would be your monthly payments? Answer all parts of the question in the text box below. Round your final answer to 2 decimal points

Answer 1

Answer to (a): Calculation of how much would you have to save annually at the end of each year for the next 42 years to reach your $5,000,000 goal assuming a 10% annual rate of return.

Future Value of Annuity = Yearly Amount * FVIFAi,n

FVIFA_i,n is the future annuity factor at i% for n period, here i is rate of interest and n refers to no. of years:

FVIFA (10%, 42 years) = (1+i)ⁿ-1/ i

= (1+0.10)⁴²-1/0.10

= 54.76369924-1/0.10

= 53.76369924/0.10

=537.6369924

Therefore;

Yearly Amount = 5000000/537.6369924

= $ 9299.96

Therefore $ 9299.96 will have to save each year for the next 42 years to reach your $5,000,000 goal.

Answer to (b): Calculation of how much would you need to invest at age 23 to have $5,000,000 in your portfolio at age 65.

Here it is assumed that rate of interest is 10% as said in part (a)

Future Amount = Invested Amount * (1+r%)ⁿ

5000000 = Invested Amount *(1+0.10)⁴²

5000000 = Invested Amount*54.76369924

Invested Amount = 5000000/54.76369924

= $ 91301.36

Therefore $ 91301.36 will have to be invested at the age of 23 to reach your goal of $5,000,000 at age of 65.

Answer to (c): Calculation of monthly payments of loan of $ 100000 at 4.5% APR, compounded monthly having 10 year amortization.

Monthly Payment = Loan Amount/ PVAF (r%, n periods)

PVAF (r%, n periods) refers to the present value annuity factor where r% is monthly rate of interest and n refers to number of periods.

PVAF(0.375%, 120 periods) = (1+r%)ⁿ-1/ (r%*(1+r%)ⁿ)

= (1+0.00375)¹²⁰-1/(0.00375*(1+0.00375)¹²⁰)

= 1.566992776-1/(0.00375*1.566992776)

= 0.566992776/0.005876223

=96.48932399

Therefore;

Monthly Payment = 100000/96.48932399

= 1036.38

Therefore, Monthly Payments of $ 1036.38 each to be made for 10 years.