Question

1. Option 1: Suppose you want to be a millionaire before you retire at age 50. How could you reach that goal? This is the question, John, an 18 years old college student, is faced with as he plans his future. Here are his options.

(Hit: Deposit a one time lump sum into an investment account and let it sit for 32 years.)

i) Assuming that the investment account earned 9.8% interest, compounded monthly, how much would John have to deposit at the start to reach his goal?

ii) Suppose that John had only $6000 to invest at the beginning, how old would John be when that investment reaches $1,000,000?

iii) Suppose again that John had only $6,000 to invest at the beginning, what interest rate would be required to meet his goal at age 50?

Note: please turn in all the exercises the following (step by step).

Answer 1

i).

Let x be the deposit which John will deposit. After 32 years, For the final amount to be 1000000, the monthly compounding formula will be x*(1+r/12)^(12*32)= x*(1+r/12)^384. So, 1000000= x*(1+9.8%/12)^384. On solving, x is 44013.28

So, John has to deposit $44013.28 at the start to reach his goal.

ii).

Let n be the time period after which the investment will be 1000000. Using the same forma, 1000000= 6000*(1+9.8%/12)^n. On solving, n will be 629 months which is 52.42 Years.

So, John will be 70.42 Years old when his investment reaches $1000000.

iii).

Let r be the interest rate. Using the same formula, we have 1000000= 6000*(1+r/12)^384. On solving, we get r is 16.09%.

So, interest rate need to be 16.09%.