Question

You have just completed the first half of one of the most challenging yet exhilarating classes of your college career. You are 19 years old. After listening to the wise words of your awesome professor and the thrilling representatives from Calm Waters Financial, you have decided being a millionaire is well within your reach. You decide you want to be a millionaire by the age of 59. You have looked around and found a mutual fund that expects an average return of 7% compounded monthly (totally feasible). QUESTION 1- If you are making your plan today and hope to start saving at the end of the month, how much do you need to deposit each month to reach your goal? QUESTION 2 - How much would you end up contributing to your million? After a bit of calculation, you decide you don’t want to wait until you are 59, and shift your goal to being a millionaire by 49. QUESTION 3-  How much will you need to invest each month now? When you see the number you realize it might be a bit to aggressive for you based on your budget. You think about it and remember that if you can find a fund yielding a high average return, you could get that payment down. QUESTION 4 - You and Google have a late night together and you find a fund that averages 12% compounded monthly. What impact does that have on your monthly payment? QUESTION 5 - How much do you contribute with these changes?

Answer 1

(1) Target Future Value = $ 1000000, Retirement Age = 59 and Initial Age = 19

Savings Tenure = (59-19) = 40 years or (40 x 12) = 480 months, Compounding Frequency: Monthly

Interest Rate = 7 %, Applicable Monthly Rate = 7 / 12 = 0.5833 %

Let the required monthly savings be $ k

Therefore, k x (1.005833)^(479) + k x (1.005833)^(478) +................+ k = 1000000

k x [{(1.005833)^(480)-1} / {(1.005833)-1}] = 1000000

k = $ 381.02

(2) Retirement Age = 49 years, Initial Age = 19 years

Savings Tenure = 49 - 19 = 30 years or (30 x 12) = 360 months

Let the required monthly savings be $ p

Therefore, p x (1.005833)^(359) + p x (1.005833)^(358) +..................+ p = 1000000

p x [{(1.005833)^(360)-1}/{(1.005833)-1}] = 1000000

p x 1219.87 = 1000000

p = 1000000 / 1219.87 = $ 819.76

(3) New Interest Rate = 12 % and Applicable Monthly Rate = 12 /12 = 1 %

let the new required monthly deposits be $ m

m x (1.01)^(359) + m x (1.01)^(358) +.................+ m = 1000000

m x [{(1.01)^(360)-1} / {(1.01)-1}] = 1000000

m x 3494.96 = 1000000

m = $ 286.13