A particular investment program involves continuously making small investments adding up to $3600 each year. If the investment pays 12%, and the account started off with an initial balance of $500, how much will the account be worth in 40 years?
A) $3,676,068
B) $3,615,313
C) $60,755
D) $3,706,068

Question

Quizplus · Accepted Answer

The future value of a continuously compounded investment can be calculated using the formula for continuous compounding: FV = P * e^(rt) + (A/r) * (e^(rt) - 1), where P is the initial principal, r is the interest rate, t is the time in years, A is the annual investment, and e is the base of the natural logarithm. Here, P = $500, r = 0.12, t = 40, A = $3600. Plugging these values into the formula gives approximately $3,676,068.

A Particular Investment Program Involves Continuously Making Small Investments Adding