Question

Determine the amount of money in an account when $15,000 is compounded continuously at an interest rate of 8.25% over a period of 25years

Answer 1

The continuously compounded interest formula is

$A=Pe^{r\cdot t}$

where A is the amount (future value), P is the principal (initial value), r is the interest rate and t is the time in years.

In our case, P=15 000, r= 0.0825 and t= 25. By substituting these values into our formula, we get

$A=15000e^{0.0825\cdot25}$

which gives

$\begin{gathered} A=15000e^{2.0625} \\ \\ A=15000\times7.86 \\ A=117984.14 \end{gathered}$

Then, the answer is $117,984.14