Question

Consider the following independent situations:

1. Mike Finley wishes to become a millionaire. His money market fund has a balance of $289,664 and has a guaranteed interest rate of 10% per year.
How many years must Mike leave that balance in the fund in order to get his desired $1,000,000?
2. Assume that Sally Williams desires to accumulate $1 million in 18 years using her money market fund balance of $250,249.
At what interest rate must Sally's investment compound annually?

Answer 1

a. Number of years = 13 years

b. Interest rate = 8%

Step-by-step explanation:

a. Present value = $289664

Interest rate = 10%

Future value = $1000000

Future Value = Present Value (1 + r)^n

1000000 = 289664 (1 + 10%)^n

(1 + 10%)^n = 1000000 / 289664

(1 + 10%)^n = 3.45227

(1.10)^n = 3.45227

Now solve for the n by taking ln both side.

So, n = 13

Thus, number of years = 13 years

b. Future value = 1000000

Present value = 250249

Time = 18 years

Future Value = Present Value (1 + r)^n

1000000 = 250249 (1 + r)^18

(1 + r)^18 = 1000000 / 250249

(1 + r)^18 = 3.99602

Now solve for the value of r.

Thus, r = 8%

Interest rate = 8%