## Financial Math: Practice Test

Created by Pamela Peterson Drake

1. Suppose you deposit \$1,000 in an account today that pays 5% interest, compounded annually. What will be the balance in the account at the end of two years if you withdraw only the interest paid on interest?
1. \$1,000.00
2. \$1,050.00
3. \$1,100.00
4. \$1,102.50

2. If I deposit \$200 in an account that pays 5% interest, compounded annually, what will be the balance in the account at the end of ten years if I make no withdrawals?
1. \$200.00
2. \$300.00
3. \$325.78
4. \$345.60

3. How much must you deposit in an account today so that you have a balance of \$1,000 at the end of five years if interest on the account is 4%, compounded quarterly?
1. \$819.54
2. \$820.35
3. \$821.93

4. Consider the cash flows associated with two investments:
```  Year Investment E  Investment F
0      -\$1,000      -\$1,000
1      +\$  100          \$ 0
2      +\$  500          \$ 0
3      +\$  650      +\$1,200
```
Which investment's cash flows have the higher present value if the discount rate is 5%?
1. Investment E
2. Investment F

5. Suppose you are offered an investment on January 1, 1996 with the following promised cash flows:

 Date promised Amount June 30, 1996 \$25 December 31, 1996 \$25 June 30, 1997 \$25 December 31, 1997 \$1,025
If you require a 6% annual percentage rate (APR) on your investments, what is the most you will be willing to pay for this investment?

1. \$879
2. \$981
3. \$1,000

6. Consider the cash flows in selections a through d. In each case, the first cash flow occurs at the end of the first period, the second cash flow at the end of the second period, and so on. Which of the following selections has the lowest present value if the discount rate is 5%?
1. \$200; \$200; \$200; \$200
2. \$0; \$0; \$0; \$875
3. \$750; \$0; \$0; \$0
4. \$50; \$50; \$50; \$700

7. Consider the cash flows in selections a through d. In each case, the first cash flow occurs at the end of the first period, the second cash flow at the end of the second period, and so on. Which of the following selections has the lowest present value if the discount rate is 10%?
1. \$100; \$100; \$100; \$100
2. \$0; \$0; \$0; \$500
3. \$350; \$0; \$0; \$0
4. \$50; \$50; \$50; \$375

8. Suppose you are offered an investment on January 1, 1994 with the following promised cash flows:

 Date promised Amount June 30, 1994 \$50 December 31, 1994 \$50 June 30, 1995 \$50 December 31, 1995 \$1,050

If you require a 6% annual percentage rate (APR) on your investments, what is the most you will be willing to pay for this investment?

1. \$965
2. \$1,030
3. \$1,074
4. \$1,200

9. The primary difference between an ordinary annuity and an annuity due is that:
1. the first cash flow in the ordinary annuity occurs immediately, whereas the first cash flow in the annuity due occurs one period in the future.
2. the first cash flow in the annuity due occurs immediately, whereas the first cash flow in the ordinary annuity occurs one period in the future.

10. If you deposit \$1,000 each year, starting today, in an account that pays 10% interest per year, compounded annually, what will be the balance in the account after you have made ten payments, assuming you make no withdrawals from the account?
1. \$10,000
2. \$15,937
3. \$17,531

11. If you deposit \$1 per month in an account that pays 12% interest, compounded monthly, what will be the balance in the account after two years if you make no withdrawals?
1. \$1.00
2. \$24.00
3. \$26.97
4. \$118.16

12. If you deposit \$100 in an account each quarter for two years, beginning next quarter, what will be the balance in the account at the end of two years if interest is 12%, compounded quarterly if you make no withdrawals?
1. \$800
2. \$889
3. \$921
4. \$1,230

13. The effective annual rate (EAR) is equal to the annual percentage rate (APR) when:
1. interest is continuously compounded.
2. interest is compounded daily.
3. interest is compounded annually.

14. In 1950, Jack-in-the-Box hamburger cost 24. In 1994, a Jack-in-the-Box hamburger cost 79. What is the effective annual increase in the price of a Jack-in-the-Box hamburger from 1950 to 1994?
1. 2.74%
2. 5.54%
3. 17.24%
4. 33.00%
5. 229.17%

15. In 1955, an order of McDonald's French fries cost 10. If McDonald's had increased the cost of its fries to keep up with inflation, an order of fries would cost 55 in 1994. Given this information on the price of fries, what is the effective annual rate of inflation over the period from 1955 to 1994?
1. 2.34%
2. 4.47%
3. 6.63%
4. 7.84%
5. 450.00%

16. If interest is compounded quarterly, then:
1. the effective annual rate of interest (EAR) is greater than the annual percentage rate (APR).
2. the annual percentage rate of interest (APR) is greater than the effective annual rate of interest (EAR).

17. Consider two investment opportunities, Tweedle Dee and Tweedle Dum. Tweedle Dee pays interest at the rate of 12% per year, compounded monthly. Tweedle Dum pays interest at the rate of 11.5% per year, compounded daily. Which investment provides the better return?
1. Tweedle Dee
2. Tweedle Dum

18. What is the effective annual rate that corresponds to a 9% annual percentage rate if interest is continuously compounded?
1. 9.00%
2. 9.38%
3. 9.42%

19. What is the effective annual rate that corresponds to a 12% annual percentage rate if interest is continuously compounded?
1. 12.00%
2. 12.68%
3. 12.75%
4. 12.83%

20. Suppose you are faced with two investment opportunities: Number 1 and Number 2. Number 1 provides an interest rate of 12% per year, compounded monthly. Number 2 provides an interest rate of 11.9%, compounded continuously. Which investment provides the better return?
1. Number 1
2. Number 2

21. The Cost U Loan Company is willing to lend you \$1,000 today. The loan is to be paid off in twenty equal annual installments of \$100 each, beginning today. What is the effective annual rate (EAR) of borrowing from Cost U Loan Company?
1. EAR < 6%
2. 6% < EAR < 8%
3. 8% < EAR < 10%
4. 10% < EAR

22. The Cost U Loan Company is willing to lend you \$1,000 today. The loan is to be paid off in twenty equal annual installments of \$100 each, beginning one year from today. What is the effective annual rate (EAR) of borrowing from Cost U Loan Company?
1. EAR < 6%
2. 6% < EAR < 8%
3. 8% < EAR < 10%
4. 10% < EAR

23. The Milken Company is offering you an investment that promises you \$1,000 at the end of ten years if you invest \$500 today. What is the annual return on this investment?
1. 0.0%
2. 7.2%
3. 10.0%
4. 100.0%

24. Suppose that you can subscribe to a magazine using either a one-year rate of \$22, a two-year rate of \$38, or a three-year rate of \$54. If want to receive this magazine for three years and if your opportunity cost of funds is 5%, which rate offers the lowest cost?
1. A three-year subscription costing \$54 and paid immediately.
2. Three one-year subscriptions, of \$22 each, paid at the beginning of each year.
3. A two-year subscription paid immediately, costing \$38, followed by a one-year subscription costing \$22 and paid at the beginning of the third year.
4. A one-year subscription paid immediately, costing \$22, followed by a two-year subscription costing \$38 and paid at the beginning of the second year.

25. Sam refuses to retire until his retirement account has a balance of at least \$300,000. Sam refuses to make any more deposits in the account. The account currently has a balance of \$200,000 and earns 6% per year, compounded semi-annually. How long does Sam have before he will retire?
1. 6.5 years
2. 7 years
3. 13 years
4. 14 years

26. At an interest rate of 6%, compounded annually, how long does it take a given sum to triple in value?
1. 17 years
2. 18 years
3. 19 years
4. 20 years

27. At an interest rate of 8%, compounded semi-annually, how long does it take a given sum to triple in value?
1. 14.5 years
2. 15 years
3. 28 years
4. 29 years

28. Chris refuses to retire until her retirement account has a balance of at least \$300,000. Chris also refuses to make any additional deposits into the account. The account currently has a balance of \$100,000 and earns 4% per year, compounded quarterly. How long does Chris have before she will retire?
1. 24 years and 3 months
2. 27 years and 9 months
3. 29 years
4. 119 years
Solutions