Practice Problem – Compound Interest

Practice Question

Intro to Finance
Time Value of Money
Compound Interest
Short Answer

Kenshi's dream is to buy a home, so he decides to start a "real estate" fund. Note that Kenshi deposited $38,937 into an investing account that pays 7.3488% compounded 12 times per year. How large will Kenshi's "real estate" fund be in 15 years?

Select the closest answer: $128,829.29, $122,694.56, $116,851.96, $113,930.66, $111,082.40

Answer +
Correct Answer: $116,851.96
Explanation +
Step 1: Highlight Relevant Information

Kenshi deposited $38,937 into an investing account that pays 7.3488% compounded monthly, and the investment will last for 15 years. His goal is to save enough to buy a $252,185 home.

Key definitions:

  • PV₀ = 38,937
  • QR (Quoted Rate) = 7.3488%
  • m = 12 compounding periods per year
  • n = 15 years

Step 2: Converting QR to Effective Annual Rate (EAR)

EAR = (1 + QR / m)m − 1
EAR = (1 + 0.073488 / 12)12 − 1
EAR ≈ 7.6015%

Step 3: Calculating Future Value of Kenshi’s Fund

FV = PV × (1 + EAR)n
FV = 38,937 × (1 + 0.076015)15
FV ≈ 38,937 × 3.0015
FV ≈ $116,851.96

Step 4: Comparing to Goal

Kenshi’s fund will grow to approximately $116,851.96. This is far short of his $252,185 home goal, so he may need to save more or adjust his timeline.