Question

Martha opened a savings account 8 years ago. The account earns 6% interest, compounded continuously. If the current balance is $500.00, how much did she deposit initially?
Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest cent.

Answer 1

To find the initial deposit (P) that Martha made, we can rearrange the formula for continuous compounding interest \( A = Pe^{rt} \).

Given:
- \( A = 500 \)
- \( r = 0.06 \) (since 6% expressed as a decimal is 0.06)
- \( t = 8 \)

We can substitute these values into the formula and solve for \( P \):

\[
500 = Pe^{0.06 \times 8}
\]

First, calculate \( e^{0.48} \) (since \( 0.06 \times 8 = 0.48 \)):

\[
e^{0.48} \approx 1.616
\]

Now substitute this value back into the equation:

\[
500 = P \times 1.616
\]

Now, solve for \( P \):

\[
P = \frac{500}{1.616} \approx 309.55
\]

Thus, the initial deposit Martha made is approximately **$309.55**.