How much more interest will be earned if $7,500 is invested for 7 years at an annual rate of 12% compounded continuously, instead of at 12% compounded quarterly? Round your answer to the nearest cent.
A)$17,372.75
B)$2,802.74
C)$213.29
D)$4,315.07
E)$5,301.40

Question

How much more interest will be earned if $7,500 is invested for 7 years at an annual rate of 12% compounded continuously, instead of at 12% compounded quarterly? Round your answer to the nearest cent. ​
A)$17,372.75
B)$2,802.74
C)$213.29
D)$4,315.07
E)$5,301.40

Quizplus · Accepted Answer

The interest earned from continuous compounding can be calculated using the formula $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm (approximately 2.71828). For quarterly compounding, the formula is $A = P(1 + \frac{r}{n})^{nt}$, where $n$ is the number of times the interest is compounded per year.For continuous compounding:- $P = \$7,500$- $r = 0.12$- $t = 7$$$A = 7500e^{0.12 \times 7} = 7500e^{0.84} \approx \$20,085.54$$For quarterly compounding:- $n = 4$ (since it's quarterly)$$A = 7500\left(1 + \frac{0.12}{4}\right)^{4 \times 7} = 7500\left(1 + 0.03\right)^{28} \approx \$19,872.25$$The difference in interest earned:$$20,085.54 - 19,872.25 = \$213.29$$

How Much More Interest Will Be Earned If $7,500 Is