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*7.86 \\ A=117984.14 \end{gathered}`

Then, the answer is $117,984.14