Question

1. Assume there is a project that will bring in $25,391.46 six years from now at the initial investment of $10,000. What will the (annual) interest rate be? Assume the interest rate compounds monthly, and round your answer by the second decimal digit using the standard rules for rounding.

2. Assume the firm invests $70,000 today at a 11% interest rates and would like to have it grow to $370,000. How many years will the investment take to grow to $370,000? Assume the interest rate compounds annually.

Answer 1

1. Initial Investment = $10000

Investment value after 6 year = 25391.46

Let r be the annual interest rate

Total Period = 6*12 = 72

10000*(1+r/12)^72 = 25391.46

--> r/12 =((25391.46/10000)^(1/72) -1) = 1.3%

--> r = 15.6%

2) Initial Investment = $70000

Value of investment after n years = $370000

r = 11%

--> 70000*(1+0.11)^n = 370000

(1.11)^n = 5.29

Taking log both sides,

nlog(1.11) = log(5.29)

n = log(5.29)/log(1.11)

n = 17.47

Therefore, it will take 17.47 years for investment to grow from $70000 to $370000 at interest rate of 11%