CFA Level IQuantitative MethodsEasy
A client deposits $5,000 at the beginning of each year for 4 years into an account that earns 6% annually. What is the value of the account at the end of year 4?
- A$20,000.00
- B$24,000.00
- C$23,185.06
- D$21,873.08
Show answer & explanationAnswer & explanation
Correct answer: C. $23,185.06
The ordinary annuity FV factor is [(1.06^4 - 1)/0.06] = 4.374616, giving FV = 5,000 x 4.374616 = $21,873.08. Because deposits occur at the beginning of each period (annuity due), multiply by (1+r): 21,873.08 x 1.06 = $23,185.06.
Why the other options are wrong
- A. This is simply 4 x $5,000 with no interest earned.
- B. This overstates growth by applying a flat 20% return incorrectly.
- D. This is the FV of an ordinary annuity (end-of-period deposits), not an annuity due.
Annuity Due Future Value
An annuity due has cash flows at the beginning of each period; its future value equals the ordinary annuity FV multiplied by (1+r).
- FV(ordinary) = PMT x [(1+r)^n - 1]/r
- FV(due) = FV(ordinary) x (1+r)
- Annuity due always has higher FV than ordinary annuity for same terms
Memory trick: Due deposits get one extra ride on interest.