How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.
A) $47.49
B) $93.15
C) $140.64
D) $2,924.71
E) $3,017.87

Question

Quizplus · Accepted Answer

Using the formula A = Pe^(rt), where A is the final amount, P is the principal, e is Euler's constant (approximately 2.71828), r is the annual interest rate, and t is the time in years:

For continuous compounding:
A = 7000e^(0.09*9) = $16,521.65

For quarterly compounding:
n = 4 (since interest is compounded quarterly)
r = 0.09/4 = 0.0225 (the quarterly interest rate)
t = 9*4 = 36 (the number of quarters in 9 years)
A = 7000(1 + 0.0225)^36 = $16,381.01

The difference in interest earned is $16,521.65 - $16,381.01 = $140.64, rounded to the nearest cent. Therefore, the best choice is C.

How Much More Interest Will Be Earned If $7,000 Is