TVM Practice Questions and Answers

QuestionWorkingsCorrect Answer
1. The future value of $500 after 3 years at 8% annual interest compounded quarterly is:Since this is a single lump sum, use the Future Value formula for compound interest.$629.50
Formula: FV = PV × (1 + i/n)^(nt)
Workings: FV = $500 × (1 + 0.08/4)^(4×3). Calculate 1 + 0.02 = 1.02. Then, 1.02^12 = 1.26824. Multiply 1.26824 by $500.
2. What is the present value of $1,000 due in 5 years at an annual interest rate of 6% compounded semi-annually?Since this is a future lump sum to be discounted back to the present, use the Present Value formula for compound interest.$743.05
Formula: PV = FV / (1 + i/n)^(nt)
Workings: PV = $1,000 / (1 + 0.06/2)^(2×5). Calculate 1 + 0.03 = 1.03. Then, 1.03^10 = 1.34392. Divide $1,000 by 1.34392.
3. The future value of an annuity with annual payments of $200, an annual interest rate of 7%, and 4 years is:Since this is a series of regular payments, use the Future Value of an Annuity formula.$885.76
Formula: FV = PMT × [(1 + i)^n – 1] / i
Workings: FV = $200 × [(1 + 0.07)^4 – 1] / 0.07. Calculate (1 + 0.07)^4 = 1.31080. Subtract 1 = 0.31080. Divide by 0.07 = 4.439. Multiply by $200.
4. Calculate the present value of an annuity with monthly payments of $50, an annual interest rate of 5%, and 3 years.Since this is a series of regular payments, use the Present Value of an Annuity formula.$1,731.85
Formula: PV = PMT × [1 – (1 + i/n)^-nt] / (i/n)
Workings: PV = $50 × [1 – (1 + 0.05/12)^-36] / (0.05/12). Calculate monthly interest rate: 0.05/12 = 0.004167. Calculate (1 + 0.004167)^-36 = 0.86804. Subtract from 1 = 0.13196. Divide by 0.004167 = 31.61. Multiply by $50.
5. What is the future value of $1,500 invested for 5 years at an annual interest rate of 10% compounded annually?Since this is a single lump sum, use the Future Value formula for compound interest.$2,415.76
Formula: FV = PV × (1 + i)^n
Workings: FV = $1,500 × (1 + 0.10)^5. Calculate (1 + 0.10)^5 = 1.61051. Multiply by $1,500.
6. The present value of an annuity due with payments of $400 per year, an annual interest rate of 8%, and 6 years is:Since this is a series of payments made at the beginning of each period, use the Present Value of an Annuity Due formula.$1,850.80
Formula: PV = PMT × [1 – (1 + i)^-n] / i × (1 + i)
Workings: PV = $400 × [1 – (1 + 0.08)^-6] / 0.08 × (1 + 0.08). Calculate (1 + 0.08)^-6 = 0.67684. Subtract from 1 = 0.32316. Divide by 0.08 = 4.039. Multiply by (1 + 0.08) = 1.08. Finally, multiply by $400.
7. What is the effective annual rate (EAR) for a nominal rate of 5% compounded monthly?To find the effective rate, use the formula for converting nominal rates to effective rates.5.12%
Formula: EAR = (1 + i/n)^(n) – 1
Workings: EAR = (1 + 0.05/12)^12 – 1. Calculate 1 + 0.05/12 = 1.004167. Then, 1.004167^12 = 1.05116. Subtract 1 = 0.05116.
8. The future value of $800 invested for 3 years at an annual interest rate of 6% compounded monthly is:Since this is a single lump sum, use the Future Value formula for compound interest.$955.24
Formula: FV = PV × (1 + i/n)^(nt)
Workings: FV = $800 × (1 + 0.06/12)^(12×3). Calculate 1 + 0.06/12 = 1.005. Raise to the power of 36 = 1.19405. Multiply by $800.
9. Calculate the present value of a single payment of $2,500 due in 4 years if the annual interest rate is 9% compounded annually.Since this is a future lump sum to be discounted back to the present, use the Present Value formula for compound interest.$1,772.58
Formula: PV = FV / (1 + i)^n
Workings: PV = $2,500 / (1 + 0.09)^4. Calculate (1 + 0.09)^4 = 1.41158. Divide $2,500 by 1.41158.
10. The future value of an ordinary annuity with payments of $250 per month, an annual interest rate of 5%, and 5 years is:Since this is a series of regular payments, use the Future Value of an Annuity formula.$15,968.51
Formula: FV = PMT × [(1 + i/n)^(nt) – 1] / (i/n)
Workings: FV = $250 × [(1 + 0.05/12)^(12×5) – 1] / (0.05/12). Calculate (1 + 0.05/12)^(60) = 1.28368 – 1 = 0.28368. Divide by 0.05/12 = 0.8333. Multiply by $250.
11. What is the present value of an ordinary annuity with payments of $600 per year, an annual interest rate of 6%, and 4 years?Since this is a series of regular payments, use the Present Value of an Annuity formula.$2,079.06
Formula: PV = PMT × [1 – (1 + i)^-n] / i
Workings: PV = $600 × [1 – (1 + 0.06)^-4] / 0.06. Calculate (1 + 0.06)^-4 = 0.79294. Subtract from 1 = 0.20706. Divide by 0.06 = 3.451. Multiply by $600.
12. The formula for calculating the future value of a lump sum compounded continuously is:Since this is continuous compounding, use the formula for continuous compounding.$1,282.00
Formula: FV = PV × e^(i × n)
Workings: FV = $1,000 × e^(0.05 × 5). Calculate e^(0.25) ≈ 1.284. Multiply by $1,000.
13. Calculate the present value of $1,200 due in 3 years at an annual interest rate of 5% compounded annually.Since this is a future lump sum to be discounted back to the present, use the Present Value formula for compound interest.$1,037.12
Formula: PV = FV / (1 + i)^n
Workings: PV = $1,200 / (1 + 0.05)^3. Calculate (1 + 0.05)^3 = 1.15763. Divide $1,200 by 1.15763.
14. What is the future value of $2,000 invested for 6 years at an annual interest rate of 7% compounded annually?Since this is a single lump sum, use the Future Value formula for compound interest.$3,001.40
Formula: FV = PV × (1 + i)^n
Workings: FV = $2,000 × (1 + 0.07)^6. Calculate (1 + 0.07)^6 = 1.50073. Multiply by $2,000.
15. The present value of an annuity with payments of $300 per year, an annual interest rate of 4%, and 10 years is:Since this is a series of regular payments, use the Present Value of an Annuity formula.$2,433.27
Formula: PV = PMT × [1 – (1 + i)^-n] / i
Workings: PV = $300 × [1 – (1 + 0.04)^-10] / 0.04. Calculate (1 + 0.04)^-10 = 0.67556. Subtract from 1 = 0.32444. Divide by 0.04 = 8.111. Multiply by $300.
16. What is the future value of $400 invested at 4% annual interest compounded monthly for 6 years?Since this is a single lump sum, use the Future Value formula for compound interest.$506.13
Formula: FV = PV × (1 + i/n)^(nt)
Workings: FV = $400 × (1 + 0.04/12)^(12×6). Calculate 1 + 0.003333 = 1.003333. Raise to the power of 72 = 1.28368. Multiply by $400.
17. Calculate the present value of an annuity due with payments of $600 per year, an annual interest rate of 9%, and 7 years.Since this is a series of payments made at the beginning of each period, use the Present Value of an Annuity Due formula.$2,811.93
Formula: PV = PMT × [1 – (1 + i)^-n] / i × (1 + i)
Workings: PV = $600 × [1 – (1 + 0.09)^-7] / 0.09, then multiply by (1 + 0.09). Calculate (1 + 0.09)^-7 = 0.52763. Subtract from 1 = 0.47237. Divide by 0.09 = 5.247. Multiply by (1 + 0.09) = 1.09. Finally, multiply by $600.
18. The future value of $1,200 invested at 5% annual interest compounded quarterly for 8 years is:Since this is a single lump sum, use the Future Value formula for compound interest.$1,537.90
Formula: FV = PV × (1 + i/n)^(nt)
Workings: FV = $1,200 × (1 + 0.05/4)^(4×8). Calculate 1 + 0.0125 = 1.0125. Raise to the power of 32 = 1.282037. Multiply by $1,200.
19. What is the present value of $750 due in 2 years at an annual interest rate of 7% compounded quarterly?Since this is a future lump sum to be discounted back to the present, use the Present Value formula for compound interest.$652.91
Formula: PV = FV / (1 + i/n)^(nt)
Workings: PV = $750 / (1 + 0.07/4)^(4×2). Calculate 1 + 0.0175 = 1.0175. Raise to the power of 8 = 1.14888. Divide $750 by 1.14888.
20. Calculate the future value of an ordinary annuity with monthly payments of $100, an annual interest rate of 6%, and 5 years.Since this is a series of regular payments, use the Future Value of an Annuity formula.$6,977.00
Formula: FV = PMT × [(1 + i/n)^(nt) – 1] / (i/n)
Workings: FV = $100 × [(1 + 0.06/12)^(12×5) – 1] / (0.06/12). Calculate (1 + 0.005)^(60) = 1.34885 – 1 = 0.34885. Divide by 0.005 = 69.770. Multiply by $100.
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