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?

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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?

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

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Other answers:

If the interest is continuously compounded, then it is this formula: \(\large A = Pe^{rt} \) \(\large 20,000 = 5,000 e^{r(10)} \) \(\large 4 = e^{10r} \) \(\large \ln 4 = \ln e^{10r} \) \(\large \ln 4 = 10r\) \(\large r = \dfrac{\ln 4}{10}\) \(\large r = 0.1386\) \(\large r = 13.86\%\)

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