Q: If you want to have $5,000 in 3 years and can invest at 6% annual simple interest, how much should you invest now?

$$P = \frac{5000}{1 + 0.06 \times 3} = 4,184.10$$

Q: A credit card has an annual interest rate of 18% compounded monthly. If you carry an average daily balance of $1,200 for a 30-day billing cycle, what is the interest charged for that cycle? (Use a 360-day year.)

$$I = 1,200 \times 0.18 \times \frac{30}{360} = 18$$

Q: If $$10,000 is $$invested at 7% compounded continuously for 6 years, what is the future value?

$$A = 10,000e$$^{0.07 \times 6}$$ = 15,049.65$$

Q: You want to have $50,000 in 15 years for your child's college fund. If you can earn 5% compounded annually, how much should you deposit each year (rounded to the nearest dollar)?

$$PMT = \frac{50,000 \times 0.05}{(1.05$$)^{15}$$ - 1} = 2,529$$

Q: A $200,000 mortgage is to be paid off in 30 years with monthly payments at 6% annual interest compounded monthly. What is the monthly payment (rounded to the nearest cent)?

$$PMT = \frac{200,000 \times 0.005}{1 - (1.005$$)^{-360}$$} = 1,199.10$$

Q: You buy a car for $$18,000 and finance it with a 5-year loan at 5% annual interest compounded monthly. What is the total interest paid over the life of the loan if the monthly payment is 339.68$$?

$$339.68 \times 60 - 18,000 = 2,380.80$$

Question 1

A loan of $2,000 is taken out at a simple interest rate of 7% per year for 9 months. What is the total amount that must be repaid at the end of the loan period?

Accepted Answer

$2,105.00

Question 2

Which formula should be used to calculate the future value $$A of a $$principal $$P$$ invested at a simple interest rate $$r$$ for $$t$$ years?

Accepted Answer

$$A = P(1 + rt)$$

Question 3

A Treasury bill (T-bill) with a maturity value of $$10,000 is purchased for 9$$,900 and matures in 180 days. Using a 360-day year, what is the annual simple interest rate earned (rounded to two decimal places)?

Accepted Answer

2.02%

Question 4

If you want to have $5,000 in 3 years and can invest at 6% annual simple interest, how much should you invest now?

Accepted Answer

$$P = \frac{5000}{1 + 0.06 	imes 3} = 4,184.10$$

Question 5

A credit card has an annual interest rate of 18% compounded monthly. If you carry an average daily balance of $1,200 for a 30-day billing cycle, what is the interest charged for that cycle? (Use a 360-day year.)

Accepted Answer

$$I = 1,200 	imes 0.18 	imes \frac{30}{360} = 18$$

Question 6

Which formula gives the future value $$A of a $$principal $$P$$ invested at an annual nominal rate $$r$$, compounded $$m$$ times per year for $$t$$ years?

Accepted Answer

$$A = P(1 + \frac{r}{m}$$)^{mt}$$

Question 7

How much will $2,500 grow to in 8 years if invested at 5% compounded quarterly?

Accepted Answer

$$A = 2,500(1 + \frac{0.05}{4}$$)^{32}$$ = 3,726.13$$

Question 8

If $$10,000 is $$invested at 7% compounded continuously for 6 years, what is the future value?

Accepted Answer

$$A = 10,000e$$^{0.07 	imes 6}$$ = 15,049.65$$

Question 9

How long will it take for an investment to double if it earns 8% compounded annually?

Accepted Answer

$$n = \frac{\ln 2}{\ln(1.08)} \approx 9.006$$ years

Question 10

Which formula gives the annual percentage yield (APY) for an account with nominal rate $$r$$ compounded $$m$$ times per year?

Accepted Answer

$$APY = (1 + \frac{r}{m}$$)^{m}$$ - 1$$

Question 11

A bank offers a CD with a nominal rate of 4.8% compounded monthly. What is the APY (rounded to three decimal places)?

Accepted Answer

4.908%

Question 12

You want to have $50,000 in 15 years for your child's college fund. If you can earn 5% compounded annually, how much should you deposit each year (rounded to the nearest dollar)?

Accepted Answer

$$PMT = \frac{50,000 	imes 0.05}{(1.05$$)^{15}$$ - 1} = 2,529$$

Question 13

A $200,000 mortgage is to be paid off in 30 years with monthly payments at 6% annual interest compounded monthly. What is the monthly payment (rounded to the nearest cent)?

Accepted Answer

$$PMT = \frac{200,000 	imes 0.005}{1 - (1.005$$)^{-360}$$} = 1,199.10$$

Question 14

You buy a car for $$18,000 and finance it with a 5-year loan at 5% annual interest compounded monthly. What is the total interest paid over the life of the loan if the monthly payment is 339.68$$?

Accepted Answer

$$339.68 	imes 60 - 18,000 = 2,380.80$$

Question 15

A retirement account requires withdrawals of $1,000 per month for 20 years. If the account earns 6% compounded monthly, what is the present value needed to fund these withdrawals?

Accepted Answer

$$PV = 1,000 	imes \frac{1 - (1 + 0.005$$)^{-240}$$}{0.005} = 139,600.18$$

Question 16

A $1,500 loan is to be repaid in 12 equal monthly payments at 1% interest per month. What is the monthly payment?

Accepted Answer

$$PMT = \frac{1,500 	imes 0.01}{1 - (1.01$$)^{-12}$$} = 134.61$$

Question 17

If you make monthly deposits of $200 into an account earning 6% compounded monthly, how much will you have after 10 years?

Accepted Answer

$$FV = 200 	imes \frac{(1 + 0.005$$)^{120}$$ - 1}{0.005} = 32,776.46$$

Question 18

A $$1,000 investment grows to 1$$,500 in 7 years with interest compounded annually. What is the annual nominal rate (rounded to two decimal places)?

Accepted Answer

$$r = (\frac{1,500}{1,000}$$)^{1/7}$$ - 1 = 0.0587 = 5.87\%$$

Mathematics of Finance: Simple Interest (College Algebra Study Notes)

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