Question

Show the work with formulas.

- How many years will it take for $100,000 to grow to $500,000 if it is invested at an annual interest rate of 9.15%? Round to the nearest 0.01.

- You are told that if you invest $5,000 per year for 35 years you will have accumulated $1,000,000. What is the annual rate of return on the latter investment? Round to the nearest 0.01%.

Answer 1

We will use TVM formula which is as follows-

Future Value = Present value*((1+interest rate)^time)

Question

We need to find how much time will it take for 100,000 to grow to 500,000 if invested at 9.15%

$500,000 = $100,000*((1+9.15%)^time)

Solving for time we get

Time = 18.38 years

Question

We need to the interest rate in this-

$1,000,000 = ($5000/((1+r)^1) + ($5000/((1+r)^2) + ($5000/((1+r)^3) +......+ ($5000/((1+r)^34) + ($5000/((1+r)^35)

Solving for r

We get r = 8.66%