Money is transferred continuously into an account at the constant rate of $900 per year. The account earns interest at the annual rate of 5% compounded continuously. How much will be in the account at the end of 4 years?
A) $2,197.52
B) $133,002.01
C) $3,985.25
D) $3,600.00

Question

Quizplus · Accepted Answer

The future value of continuous compounding with continuous payments is given by the formula: $ A = Pe^{rt} + \frac{R}{r}(e^{rt} - 1) $. Here, $ P = 0 $, $ R = 900 $, $ r = 0.05 $, and $ t = 4 $. Plugging these values into the formula gives $ A = \frac{900}{0.05}(e^{0.05 \times 4} - 1) \approx 3,985.25 $.

Money Is Transferred Continuously into an Account at the Constant