Multiple compounding (PV): Darius Miller is seeking to accumulate $50,000 in six years to invest in a real estate venture. He can earn 6.35 percent annual interest with monthly compounding in a private investment. How much will he have invest today to reach his goal? (Round to the nearest dollar.)
A) $37,527
B) $47,015
C) $34,193
D) $31,648

Question

Quizplus · Accepted Answer

Using the formula for multiple compounding (PV), we can find the present value that Darius Miller needs to invest today to reach his goal of $50,000 in six years:

PV = FV / (1 + r/n)^(n*t)

where:
FV = future value = $50,000
r = annual interest rate = 6.35%
n = number of compounding periods per year = 12 (monthly compounding)
t = number of years = 6

Plugging in the values, we get:

PV = 50000 / (1 + 0.0635/12)^(12*6)
PV = $34,193 (rounded to the nearest dollar)

Therefore, the best choice is C: $34,193.

Multiple Compounding (PV): Darius Miller Is Seeking to Accumulate $50,000