Practice Problem – Compound Interest

Practice Question

Intro to Finance
Time Value of Money
Compound Interest
Short Answer

Jake has $698.45 in an account which pays 29% compounded annually. How much more additional interest can he earn over four years if he moved his money to an account which pays 30% compounded annually?

Answer +
Correct Answer: $60.68
Explanation +
Step-by-Step Solution:

To determine how much additional interest Jake can earn by moving his money from an account paying 29% compounded annually to one paying 30% compounded annually over four years, we can follow these steps:

  1. Calculate the future value (FV) of the current account (29% compounded annually):
    - Present Value (PV) = $698.45
    - Annual interest rate (r) = 29% or 0.29
    - Number of years (t) = 4
    - FV = 698.45 × (1 + 0.29)^4
    - FV = 698.45 × (1.29)^4
    - FV = 698.45 × 2.207
    - FV ≈ 1540.92
  2. Calculate the future value (FV) of the new account (30% compounded annually):
    - PV = $698.45
    - r = 30% or 0.30
    - t = 4
    - FV = 698.45 × (1 + 0.30)^4
    - FV = 698.45 × (1.30)^4
    - FV = 698.45 × 2.8561
    - FV ≈ 1601.60
  3. Calculate the additional interest earned by moving the money:
    - Additional Interest = 1601.60 - 1540.92
    - Additional Interest ≈ 60.68
Final Answer:

Jake can earn approximately $60.68 more in additional interest over four years by moving his money to an account that pays 30% compounded annually instead of 29%.