Question

The amount of money in an account with continuously compounded interest is given by the formula A=Pe^rt, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 7.2%. Round to the nearest tenth.

9.6 yr

1 yr

7.9 yr

0.6 yr

Answer 1

You want the money in the account to double, so \(A=2P\):
\[2P=Pe^{rt}\\
2=e^{rt}\]
You're given \(r=7.2\%=0.072.\) Solve for \(t\):
\[2=e^{0.072t}\\
\ln2=\ln\left(e^{0.072t}\right)\\
\ln2=0.072t\ln e\\
\ln2=0.072t\\
t\approx\cdots\]

Answer 2

wait would you divide somewhere?

Answer 3

Yes,
\[\ln2=0.072t~\Rightarrow~t=\frac{\ln2}{0.072}\approx\cdots\]

Answer 4

so 9.6?

Answer 5

Yep

Answer 6

thank you can you help me with something else?

Answer 7

Sure, would you mind posting it as another question? In case I can't answer it, someone else may be able to help you more readily.

Answer 8

sure