Question

You have $5,000 to invest, and want it to grow to $20,000 in ten years. What interest rate would you need to find to make this possible?

Answer 1

Simple interest, compound interest, if compound, compounded how many times per year?

Answer 2

Compounded

Answer 3

The formula for compound interest is:
Total = Principal * (1 + rate) ^ years
We have to solve this for rate:
log(1 + rate) = {log(total) -log(Principal)} ÷ Years
log(1 + rate) = {log 20,000 - log 5,000} ÷ 10
log(1 + rate) = {4.3010299957 - 3.6989700043} ÷ 10
log(1 + rate) = {0.6020599914} ÷ 10
log(1 + rate) = 0.06020599914
1 + rate = 10^0.06020599914
1 + rate = 1.148698355
rate = .148698355 OR
rate = 14.8698355%

That is a very high rate because you want your money to increase 4 times in just 10 years.

Here is a calculator to check your answer.
http://www.1728.org/compint.htm

Answer 4

If the interest is continuously compounded, then it is this formula:

\(\large A = Pe^{rt} \)

\(\large 20,000 = 5,000 e^{r(10)} \)

\(\large 4 = e^{10r} \)

\(\large \ln 4 = \ln e^{10r} \)

\(\large \ln 4 = 10r\)

\(\large r = \dfrac{\ln 4}{10}\)

\(\large r = 0.1386\)

\(\large r = 13.86\%\)