Question

Mike Finley wishes to become a millionaire. His money market fund has a balance of $403,884 and has a guaranteed interest rate of 12%. How many years must Mike leave that balance in the fund in order to get his desired $1,000,000?
Assume that Sally Williams desires to accumulate $1 million in 15 years using her money market fund balance of $209,004. At what interest rate must Sallyâs investment compound annually? (Round answer to 0 decimal places, e.g. 5%.)

Answer 1

Answer:

Mike Finley

t = 7.999983133 years rounded off to 8 years

Sally Williams

r = 0.110000123 or 11.0000123% rounded off to 11.00%

Explanation:

Mike Finley

To calculate the time period it will take Mike Finley to become a millionaire, we will use the formula of future value of cash flow. The formula for future value of cash flow is as follows,

Future value = Present value * (1+r)^t

Where,

• r is the interest rate or rate of return
• t is the time period in years

Plugging in the values for Future value, present value and r in the formula, we can calculate the t to be,

1000000 = 403884 * (1+0.12)^t

1000000 / 403884  =  1.12^t

2.475958444 = 1.12^t

Taking log on both sides.

ln(2.475958444) / ln(1.12)  =  t

t = 7.999983133 years rounded off to 8 years

Sally Williams

We will use the same formula for future value of cash flows as we used above to calculate the rate at which investment should be compounded annually to grow to $1 million.

1000000 = 209004 * (1+r)^15

1000000 / 209004 = (1+r)^15

4.784597424 = (1+r)^15

Taking root of 1 on both sides.

(4.784597424)^1/15  =  (1+r)^15 * 1/15

1.110000123  =  1+r

1.110000123 - 1 = r

r = 0.110000123 or 11.0000123% rounded off to 11.00%