QUESTION 12 - 1 POINT
Angel invests in a continuously compounded account at $2.6 \%$ interest for 12 years. At the end of those 12 years, she hope to have $\$ 7500$ in her account. How much should her initial investment be to achieve this goal?
Round to the nearest dollar.
Provide your answer below:
FEEDBAC
Answer
\(\boxed{5490}\) dollars should be the initial investment.
Step 1 ：We are given that the final amount (A) is $7500, the interest rate (r) is 2.6% or 0.026 in decimal form, and the time (t) is 12 years. We need to find the initial investment (P).
Step 2 ：The formula for continuously compounded interest is \(A = P * e^{rt}\). We can rearrange this formula to solve for P: \(P = \frac{A}{e^{rt}}\).
Step 3 ：Substituting the given values into the formula, we get \(P = \frac{7500}{e^{0.026*12}}\).
Step 4 ：Calculating the above expression, we find that the initial investment should be approximately $5490.
Step 5 ：\(\boxed{5490}\) dollars should be the initial investment.
