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Present Value worksheet

Grades 11–12 · CCSS HSA.SSE.B.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Future amount: $10,000
- Annual discount rate: 5%
- Years until the amount is received: 12
- Compounding periods per year: Monthly (12)
Find: Present value
Answer
2.
Problem 2.
- Future amount: $8,000
- Annual discount rate: 5%
- Years until the amount is received: 9
- Compounding periods per year: Quarterly (4)
Find: Present value
Answer
3.
Problem 3.
- Future amount: $10,000
- Annual discount rate: 5%
- Years until the amount is received: 12
- Compounding periods per year: Semiannually (2)
Find: Present value
Answer
4.
Problem 4.
- Future amount: $7,500
- Annual discount rate: 4%
- Years until the amount is received: 11
- Compounding periods per year: Semiannually (2)
Find: Present value
Answer
5.
Problem 5.
- Future amount: $10,000
- Annual discount rate: 7%
- Years until the amount is received: 9
- Compounding periods per year: Monthly (12)
Find: Present value
Answer
6.
Problem 6.
- Future amount: $13,000
- Annual discount rate: 6%
- Years until the amount is received: 10
- Compounding periods per year: Semiannually (2)
Find: Present value
Answer
7.
Problem 7.
- Future amount: $10,000
- Annual discount rate: 5%
- Years until the amount is received: 10
- Compounding periods per year: Quarterly (4)
Find: Present value
Answer
8.
Problem 8.
- Future amount: $10,000
- Annual discount rate: 3%
- Years until the amount is received: 9
- Compounding periods per year: Annually (1)
Find: Present value
Answer
9.
Problem 9.
- Future amount: $12,000
- Annual discount rate: 4%
- Years until the amount is received: 12
- Compounding periods per year: Semiannually (2)
Find: Present value
Answer
10.
Problem 10.
- Future amount: $12,000
- Annual discount rate: 3%
- Years until the amount is received: 11
- Compounding periods per year: Annually (1)
Find: Present value
Answer

Answer key: Present Value worksheet

1. Present value: $5,494.96
1. Find the rate for each month (i): divide the yearly rate by 12, because it's applied 12 times a year
  $i$ $= \frac{0.05}{12}$ $= 0.00416667$
2. Count the periods (N): 12 a year for 12 years
  $N$ $= 12 \times 12$ $= 144$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$10,000.00}{{(1 + 0.00416667)}^{144}}$ $= $5,494.96$
2. Present value: $5,115.27
1. Find the rate for each quarter (i): divide the yearly rate by 4, because it's applied 4 times a year
  $i$ $= \frac{0.05}{4}$ $= 0.0125$
2. Count the periods (N): 4 a year for 9 years
  $N$ $= 4 \times 9$ $= 36$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$8,000.00}{{(1 + 0.0125)}^{36}}$ $= $5,115.27$
3. Present value: $5,528.75
1. Find the rate for each half-year (i): divide the yearly rate by 2, because it's applied 2 times a year
  $i$ $= \frac{0.05}{2}$ $= 0.025$
2. Count the periods (N): 2 a year for 12 years
  $N$ $= 2 \times 12$ $= 24$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$10,000.00}{{(1 + 0.025)}^{24}}$ $= $5,528.75$
4. Present value: $4,851.29
1. Find the rate for each half-year (i): divide the yearly rate by 2, because it's applied 2 times a year
  $i$ $= \frac{0.04}{2}$ $= 0.02$
2. Count the periods (N): 2 a year for 11 years
  $N$ $= 2 \times 11$ $= 22$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$7,500.00}{{(1 + 0.02)}^{22}}$ $= $4,851.29$
5. Present value: $5,335.68
1. Find the rate for each month (i): divide the yearly rate by 12, because it's applied 12 times a year
  $i$ $= \frac{0.07}{12}$ $= 0.00583333$
2. Count the periods (N): 12 a year for 9 years
  $N$ $= 12 \times 9$ $= 108$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$10,000.00}{{(1 + 0.00583333)}^{108}}$ $= $5,335.68$
6. Present value: $7,197.78
1. Find the rate for each half-year (i): divide the yearly rate by 2, because it's applied 2 times a year
  $i$ $= \frac{0.06}{2}$ $= 0.03$
2. Count the periods (N): 2 a year for 10 years
  $N$ $= 2 \times 10$ $= 20$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$13,000.00}{{(1 + 0.03)}^{20}}$ $= $7,197.78$
7. Present value: $6,084.13
1. Find the rate for each quarter (i): divide the yearly rate by 4, because it's applied 4 times a year
  $i$ $= \frac{0.05}{4}$ $= 0.0125$
2. Count the periods (N): 4 a year for 10 years
  $N$ $= 4 \times 10$ $= 40$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$10,000.00}{{(1 + 0.0125)}^{40}}$ $= $6,084.13$
8. Present value: $7,664.17
1. Find the rate for each year (i): divide the yearly rate by 1, because it's applied 1 time a year
  $i$ $= \frac{0.03}{1}$ $= 0.03$
2. Count the periods (N): 1 a year for 9 years
  $N$ $= 1 \times 9$ $= 9$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$10,000.00}{{(1 + 0.03)}^{9}}$ $= $7,664.17$
9. Present value: $7,460.66
1. Find the rate for each half-year (i): divide the yearly rate by 2, because it's applied 2 times a year
  $i$ $= \frac{0.04}{2}$ $= 0.02$
2. Count the periods (N): 2 a year for 12 years
  $N$ $= 2 \times 12$ $= 24$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$12,000.00}{{(1 + 0.02)}^{24}}$ $= $7,460.66$
10. Present value: $8,669.06
1. Find the rate for each year (i): divide the yearly rate by 1, because it's applied 1 time a year
  $i$ $= \frac{0.03}{1}$ $= 0.03$
2. Count the periods (N): 1 a year for 11 years
  $N$ $= 1 \times 11$ $= 11$
3. Work the future amount back to today by undoing one period of growth for every period you wait
  $\frac{$12,000.00}{{(1 + 0.03)}^{11}}$ $= $8,669.06$