When your first child is born, you begin to save for college by depositing $600 per month in an account paying 6% interest per year. With a continuous stream of investment and continuous compounding, how much will you have accumulated in the account by the time your child enters college 18 years later Round your answer to the nearest cent.
A)$233,361.55
B) $353,361.55
C) $1,166.81
D) $473,361.55
E) $79,248.54

Question

When your first child is born, you begin to save for college by depositing $600 per month in an account paying 6% interest per year. With a continuous stream of investment and continuous compounding, how much will you have accumulated in the account by the time your child enters college 18 years later  Round your answer to the nearest cent. 
A)$233,361.55
B) $353,361.55
C) $1,166.81
D) $473,361.55
E) $79,248.54

Quizplus · Accepted Answer

The correct answer can be found using the formula for the future value of a series with continuous compounding: $FV = P \times \frac{e^{rt}-1}{r}$, where $P$ is the monthly payment, $r$ is the monthly interest rate, and $t$ is the time in months. Given $P = $600$, $r = 0.06/12$ per month, and $t = 18 \times 12$ months, the calculation yields approximately $233,361.55.

When Your First Child Is Born, You Begin to Save