Question

Patty has $10 000 that she would like to invest. She has found an investment that will pay 5.6% compounded monthly.a)Use the Rule of 72 to estimate the length of time it will take for her investment to double.b)Use the TVM solver to find the exact amount of time it will take for her investment to double.

Answer 1

a)

The Rule of 72 states that the time required to double the investment (in years) is given by the formula below:

`\text{time to double}=(72)/(r)`

Where r is the investment rate in percentage.

So, for r = 5.6, we have:

`\text{time to double}=(72)/(5.6)=12.86\text{ years}`

Therefore the time needed to double is 12.86 years.

b)

In order to calculate the exact time to double, let's use the formula below:

`A=P(1+(r)/(n))^(nt)`

Where A is the final amount after t years, P is the principal (initial amount), r is the interest rate and n is how many times the interest is compounded in a year.

So, for A = 2P, r = 0.056 and n = 12, we have:

`\begin{gathered} 2P=P(1+(0.056)/(12))^(12t) \\ 2=(1+0.0046667)^(12t) \\ 2=1.0046667^(12t) \\ \ln (2)=\ln (1.0046667^(12t))^{} \\ \ln (2)=12t\cdot\ln (1.0046667) \\ 12t=(\ln (2))/(\ln (1.0046667)) \\ 12t=(0.693147)/(0.0046558) \\ 12t=148.878 \\ t=12.4 \end{gathered}`

Therefore the time needed to double is 12.4 years.