Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent.
A) 7.44 %/yr
B) 7.32 %/yr
C) 6.39 %/yr
D) 8.01 %/yr
E) 7.78 %/yr

Question

Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 3 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent. ​
A) 7.44 %/yr
B) 7.32 %/yr
C) 6.39 %/yr
D) 8.01 %/yr
E) 7.78 %/yr

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = \frac{\ln(A/P)}{t}$. Plugging in the given values: $A = 5000$, $P = 4000$, and $t = 3$, we get $r = \frac{\ln(5000/4000)}{3}$. Calculating this gives $r \approx 0.0744$ or $7.44\%$.

Find the Interest Rate Needed for an Investment of $4,000