Asked by Jennifer McCray on Jun 09, 2024
Verified
An investment of $1250 is made in an account that compounds interest continuously. After years 10 the balance in the account is $2,040.40. To the nearest tenth of a percent, what is the annual interest rate for this account?
A) 6.3%6.3 \%6.3%
B) 10.7%10.7 \%10.7%
C) 4.9%4.9 \%4.9%
D) 0.5%0.5 \%0.5%
E) 2.1%2.1 \%2.1%
Annual Interest Rate
The percentage rate charged or paid over a period of one year for a loan or investment.
Compounds Interest Continuously
The process of calculating interest on both the initial principal and the accumulated interest from previous periods, assumed to be compounded infinitely often per period.
Nearest Tenth
Rounding a number to one decimal place, or to the closest tenth.
- Determine annual interest rates from given financial scenarios.
Verified Answer
MS
Mohit sarrafJun 10, 2024
Final Answer :
C
Explanation :
The formula for continuous compounding is $A=P e^{rt}$ where $A$ is the ending balance, $P$ is the principal, $r$ is the annual interest rate in decimal form, and $t$ is the time in years.
Plugging in the given values, we get $2040.40=1250 e^{10r}$. Solving for $r$, we get $r\approx 0.04915$. Converting to a percentage, we get $\boxed{\textbf{(C)}\ 4.9\%}$.
Plugging in the given values, we get $2040.40=1250 e^{10r}$. Solving for $r$, we get $r\approx 0.04915$. Converting to a percentage, we get $\boxed{\textbf{(C)}\ 4.9\%}$.
Learning Objectives
- Determine annual interest rates from given financial scenarios.