Decreasing Annuities (Present Value) — Practice Quiz

A Financial Math cheat sheet for Decreasing Annuities (Present Value) — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. A person wants to withdraw \$2,000 at the end of each month for 20 years from an account that earns $5\%$ annual interest compounded monthly. How much money must be in the account today to support these withdrawals? Round to the nearest cent.

   • \$303,050.63
   • \$480,000.00
   • \$24,924.42
   • \$-822,067.34

   Answer: \$303,050.63

2. You have \$500,000 in a retirement account that earns $6\%$ annual interest compounded quarterly. If you want to withdraw equal amounts at the end of each quarter for 25 years until the account is depleted, how much can you withdraw each quarter? Round to the nearest cent.

   • \$9,685.29
   • \$5,000.00
   • \$39,113.36
   • \$-2,185.29

   Answer: \$9,685.29

3. In the present value of an annuity formula, $PV = PMT \times \frac{1 - (1 + i)^{-N}}{i}$, what does $N$ represent?

   • The annual interest rate.
   • The number of compounding periods per year.
   • The total number of payment periods.
   • The present value of the annuity.

   Answer: The total number of payment periods.

4. Scenario A: You want to withdraw \$1,500 at the end of each month for 15 years from an account earning $4\%$ annual interest compounded monthly.\nScenario B: You want to withdraw \$1,200 at the end of each month for 20 years from an account earning $4\%$ annual interest compounded monthly.\nHow much more money do you need to have today for Scenario A compared to Scenario B? Round to the nearest cent.

   • \$4,761.99
   • \$-4,761.99
   • \$400,814.45
   • \$369.19

   Answer: \$4,761.99

5. A trust fund is set up to pay out \$10,000 at the end of every six months for 10 years. If the fund earns $3\%$ annual interest compounded semi-annually, what is the present value of this annuity? Round to the nearest cent.

   • \$171,686.39
   • \$1,035,617.53
   • \$85,302.03
   • \$-231,236.67

   Answer: \$171,686.39

6. You have \$300,000 in an investment account. You want to withdraw equal amounts at the end of each month for 15 years. If the account earns $4.5\%$ annual interest compounded monthly, how much can you withdraw each month? Round to the nearest cent.

   • \$2,294.98
   • \$1,666.67
   • \$27,934.14
   • \$-1,169.98

   Answer: \$2,294.98

7. Which of the following formulas correctly represents the present value ($PV$) of an annuity, where $PMT$ is the periodic payment, $i$ is the periodic interest rate, and $N$ is the total number of periods?

   • $PV = PMT \times \frac{1 - (1 + i)^{-N}}{i}$
   • $PV = PMT \times \frac{(1 + i)^{N} - 1}{i}$
   • $PV = PMT \times (1 + i)^{N}$
   • $PV = PMT \times N \times (1 + i)$

   Answer: $PV = PMT \times \frac{1 - (1 + i)^{-N}}{i}$

8. A person needs \$3,000 at the end of each quarter for 10 years. An account earning $5\%$ annual interest compounded quarterly is used. How much more is the total amount withdrawn than the initial present value needed in the account? Round to the nearest cent.

   • \$26,019.20
   • \$-26,019.20
   • \$120,000.00
   • \$93,980.80

   Answer: \$26,019.20

9. You want to set up a fund that will provide your grandchild with \$500 at the end of each month for 5 years, starting when they turn 18. If the fund earns $3.6\%$ annual interest compounded monthly, how much money do you need to deposit into the fund today to achieve this? Round to the nearest cent.

   • \$27,417.45
   • \$2,251.15
   • \$30,000.00
   • \$-32,815.80

   Answer: \$27,417.45

10. In the present value of an annuity formula, $PV = PMT \times \frac{1 - (1 + i)^{-N}}{i}$, if the annual interest rate is $r$ and interest is compounded $n$ times per year, how is the periodic interest rate $i$ calculated?

    • $i = r \times n$
    • $i = r / n$
    • $i = r + n$
    • $i = r - n$

    Answer: $i = r / n$