Q: A savings account offers an annual interest rate of 3% compounded monthly. If you deposit $$\2$$,000$ into the account, what will be the balance after 5 years? Use the compound interest formula.

$$A = 2000(1 + \frac{0.03}{12}$$)^{12 \times 5}$$ = 2000(1 + 0.0025$$)^{60}$$ \approx \2$$,348.85$

Q: A corporate bond pays interest semiannually at an annual rate of 4%. If you invest $$\10$$,000$ for 3 years, what is the accumulated balance at maturity? Use the compound interest formula.

$$A = 10000(1 + \frac{0.04}{2}$$)^{2 \times 3}$$ = 10000(1 + 0.02$$)^{6}$$ \approx \11$$,261.56$

Q: A T-note is purchased for $$\5$$,000$ at an annual interest rate of 2.5%, compounded semiannually, for 10 years. What is the accumulated balance at maturity?

$$A = 5000(1 + \frac{0.025}{2}$$)^{2 \times 10}$$ = 5000(1 + 0.0125$$)^{20}$$ \approx \6$$,414.13$

Q: A credit card loan of $$\1$$,500$ carries an annual interest rate of 18%, compounded monthly. If no payments are made, what is the balance after 2 years?

$$A = 1500(1 + \frac{0.18}{12}$$)^{12 \times 2}$$ = 1500(1 + 0.015$$)^{24}$$ \approx \2$$,035.36$

Q: If $$P = \3$$,000$$, R = 0.05$, and T = 4$ years, what is the accumulated balance using simple interest?

$$A = 3000(1 + 0.05 \times 4) = 3000(1 + 0.20) = \3$$,600$

Q: A certificate of deposit (CD) offers 2.8% annual interest compounded quarterly. If you invest $$\8$$,000$ for 6 years, what is the accumulated balance?

$$A = 8000(1 + \frac{0.028}{4}$$)^{4 \times 6}$$ = 8000(1 + 0.007$$)^{24}$$ \approx \9$$,456.36$

Q: A savings bond (EE type) is purchased for $$\1$$,000$ at a fixed annual rate of 3%, compounded semiannually, for 7 years. What is the accumulated balance?

$$A = 1000(1 + \frac{0.03}{2}$$)^{2 \times 7}$$ = 1000(1 + 0.015$$)^{14}$$ \approx \1$$,231.68$

Question 1

A savings account offers an annual interest rate of 3% compounded monthly. If you deposit $$\2$$,000$ into the account, what will be the balance after 5 years? Use the compound interest formula.

Accepted Answer

$$A = 2000(1 + \frac{0.03}{12}$$)^{12 	imes 5}$$ = 2000(1 + 0.0025$$)^{60}$$ \approx \2$$,348.85$

Question 2

Which of the following financial products is most likely to use continuous compounding for calculating interest?

Accepted Answer

A high-frequency trading account

Question 3

A corporate bond pays interest semiannually at an annual rate of 4%. If you invest $$\10$$,000$ for 3 years, what is the accumulated balance at maturity? Use the compound interest formula.

Accepted Answer

$$A = 10000(1 + \frac{0.04}{2}$$)^{2 	imes 3}$$ = 10000(1 + 0.02$$)^{6}$$ \approx \11$$,261.56$

Question 4

Which formula would you use to calculate the total interest earned on a simple interest loan?

Accepted Answer

$$I = PRT$$

Question 5

A T-note is purchased for $$\5$$,000$ at an annual interest rate of 2.5%, compounded semiannually, for 10 years. What is the accumulated balance at maturity?

Accepted Answer

$$A = 5000(1 + \frac{0.025}{2}$$)^{2 	imes 10}$$ = 5000(1 + 0.0125$$)^{20}$$ \approx \6$$,414.13$

Question 6

Which of the following statements about I bonds is TRUE?

Accepted Answer

I bonds always carry an interest rate higher than the inflation rate.

Question 7

A credit card loan of $$\1$$,500$ carries an annual interest rate of 18%, compounded monthly. If no payments are made, what is the balance after 2 years?

Accepted Answer

$$A = 1500(1 + \frac{0.18}{12}$$)^{12 	imes 2}$$ = 1500(1 + 0.015$$)^{24}$$ \approx \2$$,035.36$

Question 8

Which financial product is LEAST likely to use simple interest for its calculations?

Accepted Answer

Savings account

Question 9

If $$P = \3$$,000$$, R = 0.05$, and T = 4$ years, what is the accumulated balance using simple interest?

Accepted Answer

$$A = 3000(1 + 0.05 	imes 4) = 3000(1 + 0.20) = \3$$,600$

Question 10

Which of the following is NOT a characteristic of a municipal bond?

Accepted Answer

Interest is compounded monthly.

Question 11

A certificate of deposit (CD) offers 2.8% annual interest compounded quarterly. If you invest $$\8$$,000$ for 6 years, what is the accumulated balance?

Accepted Answer

$$A = 8000(1 + \frac{0.028}{4}$$)^{4 	imes 6}$$ = 8000(1 + 0.007$$)^{24}$$ \approx \9$$,456.36$

Question 12

Which formula is used to calculate the accumulated balance for continuous compounding?

Accepted Answer

$$A = Pe$$^{rT}$$

Question 13

A savings bond (EE type) is purchased for $$\1$$,000$ at a fixed annual rate of 3%, compounded semiannually, for 7 years. What is the accumulated balance?

Accepted Answer

$$A = 1000(1 + \frac{0.03}{2}$$)^{2 	imes 7}$$ = 1000(1 + 0.015$$)^{14}$$ \approx \1$$,231.68$

Question 14

Which of the following is TRUE about T-bonds?

Accepted Answer

T-bonds carry a term of either 20 or 30 years.

Question 15

A savings account compounds interest monthly at an annual rate of 2.4%. If you deposit $$\5$$,000$, what is the total interest earned after 3 years?

Accepted Answer

$$A = 5000(1 + \frac{0.024}{12}$$)^{12 	imes 3}$$ = 5000(1 + 0.002$$)^{36}$$ \approx \5$$,373.36$$; 	ext{Interest} = 5,373.36 - 5,000 = \373.36$

Question 16

Which website is used to purchase government bonds or treasuries?

Accepted Answer

www.treasurydirect.gov

Question 17

A $$\2$$,500$$ investment in a savings account earns 2.5% interest compounded monthly. What is the formula to calculate the balance after t$ years?

Accepted Answer

$$A = 2500(1 + \frac{0.025}{12}$$)^{12t}$$

Question 18

Which of the following statements about savings bonds is FALSE?

Accepted Answer

Savings bonds are always compounded monthly.

Question 19

A $$\4$$,000$ investment is compounded continuously at an annual rate of 3.2% for 8 years. What is the accumulated balance?

Accepted Answer

$$A = 4000e$$^{0.032 	imes 8}$$ = 4000e$$^{0.256}$$ \approx \5$$,163.36$

Mathematical Models in Finance: Simple, Compound, and Continuous Interest

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