Question

Calculating number of periods?How long will an initial bank deposit of $10,000 grow to $23,750 at 5% annual compound interest?

Answer 1

For an initial amount P with an annually compounded interest rate r, after t years the total amount A is is given by:

`A=P(1+r)^t`

Then we have:

`\begin{gathered} (A)/(P)=(1+r)^t \\ \ln(A)/(P)=t\ln(1+r) \\ t=(\ln(A)/(P))/(ln(1+r)) \end{gathered}`

For P = $10,000, A = $23,750 and r = 0.05, we have:

`t=(\ln(23750)/(10000))/(\ln(1+0.05))\approx17.73\text{ years}`