Question

What rate of interest compounded annually is required to double an investment in 29 years? The rate of interest required is ?

Answer 1

Use the following formula for the final amount after t years:

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

where,

P: principal investment

A = 2P (because you are interested in doubling the investment)

r: interest rate in decimal form = ?

t: time = 29

n: times at year for the compond interest = 1

Replace the previous values of the parameters into the formula for A and solve for r, as follow:

`\begin{gathered} 2P=P(1+(r)/(1))^(1\cdot29) \\ 2=(1+r)^(29) \\ \sqrt[29]{2}=1+r \\ r=\sqrt[29]{2}-1 \\ r\approx0.024 \end{gathered}`

Then, r is approximately 0.024, which corresponds to an interest rate of approximately 2.4%