Question

Multiple compounding: 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 the number.)

a. $47,015

b. $37,527

c. $34,193

d. none of the answers is correct.

e. $31,648

Answer 1

Formula for compound interest can be used to calculate principal amount as:

A = P x (1 + i)ⁿ

P = A/(1+ i)ⁿ

Where,
   P = principle amount

   A = Amount after maturity = $ 50,000
   i = Compound interest = 6.35 % p.a. or 0.0635/12 = 0.005292 p.m.
   n = Number of periods = 6 years x 12 = 72 periods

Putting the values in the above formula we get,

P = $ 50,000/(1 + 0.005292)⁷²

   = $ 50,000/(1.005292)⁷²

   = $ 50,000/1.462278

   = $ 34,193.225 or $ 34,193

Hence option “c. $ 34,193” is correct answer.