Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A financial advisor is explaining compound interest. An initial investment of $5,000 earns 4% interest compounded annually. What will be the value of the investment after 3 years?
- A$5,600.00
- B$5,624.32
- C$5,632.40
- D$5,640.73
Show answer & explanationAnswer & explanation
Correct answer: B. $5,624.32
The formula for compound interest is A = P(1 + r)^t, where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), and t is the number of years. Year 1: $5,000 * (1 + 0.04) = $5,000 * 1.04 = $5,200. Year 2: $5,200 * 1.04 = $5,408. Year 3: $5,408 * 1.04 = $5,624.32.
Why the other options are wrong
- A. This is simple interest ($5000 + $5000*0.04*3 = $5000 + $600 = $5600).
- C. This might result from a calculation error in one of the compounding steps.
- D. This might result from a calculation error or rounding at an intermediate step.
Compound Interest (Annual)
Compound interest is interest calculated on the initial principal and also on the accumulated interest from previous periods. Annually compounded means interest is calculated once per year.
- A = P(1 + r)^t is the formula.
- Interest is added to the principal before the next period's calculation.
- Leads to exponential growth over time.
Memory trick: Principal plus rate, power of time, makes your money climb!