Name ________________________________ Date ______________ Class ____________
| Section 3-1 Simple Interest |
Goal: To solve problems involving simple interest
(Unless otherwise noted, round monetary answers to the nearest dollar, percents to two decimal places when written as a percentage, and time to the nearest tenth of a year.)
- If Ms. Gonzalez borrows $500 for 2 years from a bank that charges 3% annual simple interest, how much interest will she owe at the end of the two years? How much (in total – interest + principal) will she pay to the bank at the end of the 2 years?
Ms. Gonzalez will have to pay $530 after 2 years.
- If Mr. Xu borrows $3000 for 3 years from a bank that charges 2% annual simple interest, how much interest will he owe at the end of the three years? How much will Mr. Xu have to pay to the bank at the end of the three years?
Mr. Xu will have to pay the bank $3180 after 3 years.
- Mr. and Mrs. Smith are running short of money this month and they decide to borrow $1000 from the bank and repay the money in 6 months when they get their income tax refund check. The bank charges 8% annual simple interest. How much interest will they owe at the end of the six months? How much will they have to pay to the bank at the end of the 6 months?
Mr. and Mrs. Smith will have to pay $1040 after 6 months.
- Joe is borrowing $800 from his parents in order to finish paying his tuition bill. His parents agree to the loan if Joe will repay the money at the end of nine months. His parents will charge him 5% annual simple interest. How much interest will Joe owe his parents? How much will Joe have to pay his parents at the end of the nine months?
Joe will have to pay $830 after 9 months.
- Find the amount needed to pay off a simple interest loan of $3000 at 6% for 1½ years.
You will need $3270 to pay off the loan in 1.5 years.
- Find the amount needed to pay off a simple interest loan of $2000 at 10.5% for 3 years.
You will need $2630 to pay off the loan in 3 years.
- What amount needs to be invested today at 6% simple interest in order to have $4000 in 2 years?
You will need approximately $3571 to have $4000 in 2 years.
- What amount needs to be invested today at 3.5% simple interest in order to have $500 in 6 months?
You will need approximately $491 to have $500 in 0.5 years.
- Fred would like to buy a new computer but only has $600 and a new computer costs $800. He can invest the $600 in an account that pays 2% simple interest. How long will it be before Fred can buy the new computer? Do you think the same computer will be offered at the same price when he has saved the additional $200? Why or why not?
It will take 12 years 8 months for Fred to save the additional $200. Computers change so quickly that the same computer will not be offered at the same price; in fact a better one might be offered at a cheaper price.
- Mary has $2700 in a simple interest account paying 4.5%. She would like to have $3000 for a down-payment on a new car. How long will it take Mary to have $3000 in the account?
It will take approximately 2.5 years for Mary to save the $3000.
- Mr. Wong’s daughter needs to borrow $700 from him to her textbooks. He agrees to the loan and tells her that she must pay $750 back in 6 months. What simple interest rate is Mr. Wong charging his daughter?
Mr. Wong is charging his daughter a simple interest rate of approximately 14.29%.
- Charlie is due a tax refund of $800. A tax service will give him the money two months early, but will charge $50 up front to do so. What annual simple interest rate is the tax service charging him?
The tax service is charging Charlie a simple interest rate of approximately 37.5%.
- Mr. Jones goes to a check-cashing business to get money before his paycheck is due. The business charges him $25 up front to loan him the money one week before payday. If his paycheck is for $550, what annual simple interest rate is the business charging him?
The business is charging Mr. Jones a simple interest rate of approximately 236.36%.
- A late charge on a utility bill can be interpreted as an interest charge. If John’s water bill is $85 with a $2.50 charge for being late, what annual simple interest rate is being charged if John pays the bill 2 weeks late?
The utility company is charging John a simple interest rate of approximately 76.47%.
- A man used his motorcycle as collateral on a $325 loan from a pawn shop for 3 months. The pawnshop charge was $33. What annual simple interest rate does the pawnshop charge?
The pawnshop is charging the man a simple interest rate of approximately 40.62%.
Name ________________________________ Date ______________ Class ____________
| Section 3-2 Compound and Continuous Compound Interest |
Goal: To solve problems involving compound interest
(Unless otherwise noted, round monetary answers to the nearest dollar, percents to two decimal places when written as a percentage, and time to the nearest year.)
- Suppose that $2000 is invested in an account paying 1% annual interest. Compare the balance after 20 years using simple interest and compound interest (compounded once a year) formulas.
Compounding the interest will result in $40 more interest.
- If $5000 is invested in an account that pays 2% annual compounded interest, compare the amount in the account after 10 years if the interest is compounded:
- a) semiannually (twice a year)
- b) quarterly ( four times a year)
- c) monthly (twelve times a year)
- d) continuously
- a) b)
- c) d)
- If $1500 is invested in an account that pays 4% annual interest compounded semiannually for 4 years, find the amount of interest earned each year and use the results to fill in the following chart. (Round monetary amounts to nearest penny.)
| Compound Period (at end of year) | Amount Of Interest | Amount In Account (at the end of the year) |
| 1 | $60.60 | $1560.60 |
| 2 | $63.05 | $1623.65 |
| 3 | $65.60 | $1689.25 |
| 4 | $68.25 | $1757.50 |
- You are saving for the down-payment on a house and plan to buy the house in 5 years. How much would you need to invest in an account that pays 4.5% compounded monthly in order to have $10,000 for your down-payment?
You would need to invest approximately $7989 in order to have $10,000 after 5 years
- Before you invest your money in the account in problem 4, you find another bank that pays 4.75% compounded quarterly. Will this account allow you to invest more or less money than the account in problem 4?
You would need to invest approximately $7897 (or $92 less) in order to have $10,000 after 5 years
- Joe has inherited $6000 and would like to use the money for buying property. If he needs $7000 for the investment, how long would he have to wait to buy property if he invests the money in an account that pays 3.5% compounded weekly?
It would take approximately 4.4 years to accumulate the $7000 for the investment.
- Susan invests $2500 for 3 years in an account paying 3.5% annual interest compounded monthly. At the end of that time she moves the money to a different account that pays 4% annual interest compounded quarterly, where it stays for an additional 2 years. What is the value of the account at the end of that time?
Susan would have approximately $3006 in her account after the 5 years.
- Robert invests $500 in a 9-month Certificate of Deposit (CD) that pays 3.8% annual interest compounded monthly. At the end of the 9 months he moves the money plus the interest it has earned to another CD for 6 months that pays 4% compounded monthly. What is the value of the account at the end of the time?
Robert would have approximately $525 in his account after the 15 months.
- By comparing their APYs, decide which is better: an investment at 4.26% compounded monthly, an investment at 4.3% compounded quarterly, or an investment at 4.38% compounded semiannually?
Based on the APY values, the 4.38% compounded semiannually is the best investment option.
- Joel can choose between two different banks to invest his money. Bank A offers 5.9% interest compounded quarterly. Bank B offers 5.82% interest compounded monthly. Find the APY of each investment so that you can tell Joel in which bank it is better for him to invest.
Based on the APY values, Bank A, 5.90% compounded quarterly is the better investment option.
- To accumulate $20,000 on your daughter’s 18th birthday, how much must you invest on her second birthday in a CD paying 4% compounded quarterly?
You would need to invest approximately $10,579 on her second birthday.
- To accumulate $15,000 on your son’s 20th birthday, how much must you invest on his 5th birthday in a CD paying 2.25% compounded daily?
You would need to invest approximately $10,704 on his fifth birthday.
Name ________________________________ Date ______________ Class ____________
| Section 3-3 FV of an Annuity; Sinking Funds |
Goal: To calculate future values of annuities and solve problems involving sinking funds
(Unless otherwise noted, round monetary answers to the nearest dollar, percents to two decimal places when written as a percentage, and time to the nearest year.)
- a) Suppose you deposit $1500 each year for 15 years in a savings account paying 4% compounded annually. How much would the account contain after 15 years? How much of the FV did you actually contribute?
If you could double only one of these which would benefit you more?
- b) The amount invested. How much of the FV did you actually contribute?
- c) The interest rate. How much of the FV did you actually contribute?
- d) The time. How much of the FV did you actually contribute?
- e) Write a short paragraph describing the results of parts a) – d).
Doubling the time gives the largest future value, but doubling the interest gives the best rate of return.
- Suppose you are only able to contribute $600 a year to the account described in #1a). Answer parts a) – d) of #1 based on the $600 per year contribution.
- Julia deposits $75 at the end of each quarter for 20 years into an account paying 2.8% annual interest compounded quarterly.
- How much is in the account at the end of 20 years?
- How much did Julia actually contribute to the account?
- How much interest did the account earn in those 20 years?
- George deposits $75 at the end of each quarter for 40 years into an account paying 2.8% annual interest compounded quarterly.
- How much is in the account at the end of 40 years?
- How much did George actually contribute to the account?
- How much interest did the account earn in those 40 years?
- Mr. and Mrs. Lopez have a new son and decide to start an account (sinking fund) for his college education. They decide to put $100 into the account each month. The account pays 5% annual interest compounded monthly. They start this account when he is 2 years old. How much will be in the account when the child is 18 years old?
- Mr. and Mrs. Lopez then have a daughter and start an account for her when she is born. They decide to put $120 into the account each month. Her account pays 4.5% compounded monthly. How much will be in the account when she is 18?
- John and Sally would like to buy a house in 4 years. In order to have money for a down- payment they decide to save $250 a month in an account (sinking fund) that pays 5.5% annual interest compounded monthly. How much money will they have in the account at the end of the four years?
In order to have the size house they would like, John and Sally decide they need to save 2 more years. How much will be in the account if they continue to save for two more years?
- Mr. Johnson decides when is 40 years old to start saving for retirement. He begins depositing $200 a month into an account that pays 3.75% compounded monthly. How much will be in the account if he retires when he is 60? if he retires when he is 65? if he retires when he is 70?
At 60 years At 65 years
At 70 years
- In order to have $40,000 in an account for their child’s college education, how much would a couple need to deposit in a sinking fund each quarter if the account pays 4% annual interest rate compounded quarterly? The couple begins saving when the child is 5 years old and will begin college when he is 18.
The payment required would be approximately $590 per quarter.
- If the couple decide they will need $60,000 for their child’s education, how much would they need to deposit each quarter in the same account described in #9 if they begin saving when the child is born.
The payment required would be approximately $573 per quarter.
Name ________________________________ Date ______________ Class ____________
| Section 3-4 PV of an Annuity; Amortization |
Goal: To find the present value of annuities and solve problems involving amortization
(Unless otherwise noted, round monetary answers to the nearest dollar, percents to two decimal places when written as a percentage, and time to the nearest year.)
- Sam makes a deal to pay $400 a month for 3 years on a car loan at 4.2% annual interest compounded monthly to pay for a car.
- What is the present value of the car?
- How much will Sam make in payments for the car?
- How much interest will he pay on the car loan?
- Emma makes a deal to pay $200 a month for 5 years on a car loan at 3.6% annual interest compounded monthly to pay for the car.
- What is the present value of the car?
- How much will Emma make in payments for the car?
- How much interest will she pay on the car loan?
- A car dealer, figuring interest at 5.5% compounded monthly, offers to sell you a new car if you trade in your car which is worth $6000 and agree to pay $350 every month for the next three years.
- What is the cash value of the car today?
- How much total interest would you pay with this deal?
- Another car dealer, figuring interest at 4.8% compounded monthly, offers to sell you a new car if you trade in your car which is worth $6000, pay an additional $1000 down, and agree to pay $400 for the next two years.
- What is the cash value of the car today?
- How much total interest will you pay with this deal?
- Which is a better deal, the one from Problem 3 or from Problem 4? Write a short paragraph to give the advantages and disadvantages of each deal.
The better deal is in Problem 4 because you will pay less interest and only make 24 payments. The disadvantage is you will pay more money per month and you need an additional $1000 for the down payment.
- Mark and Natalie want to buy a house selling for $120,000. They will put $20,000 down as a down payment and finance $100,000.
- If the bank offers a 30-year mortgage at 5.4% annual interest compounded monthly, what will their monthly payment be?
- Approximately how much interest will they pay if they make all the loan payments on time?
- Jeff and Theresa are buying a $96,000 house and putting 25% down. The bank is offering a 20-year loan at 7.5% compounded monthly.
- What is the loan amount?
- What will the monthly payment be?
- What is the (approximate) total amount of interest paid during the term of the loan?
- Wake and Elizabeth are buying a $130,000 house and putting 15% down. The bank is offering a 30-year loan at 7.74% compounded monthly.
- What is the loan amount?
- What will the monthly payment be?
- What is the (approximate) total amount of interest paid during the term of the loan?
(For problems 8 – 10 round monetary answers to nearest penny.)
- Margaret buys new stereo equipment for $500. The store agrees to finance the purchase price for 4 months at 12% annual interest rate compounded monthly, with approximately equal payments at the end of each month.
Her first 3 monthly payments will be $128.14. The amount of the fourth payment will be $128.14 or less (depending on the balance after the third payment). Use this information to complete the amortization schedule below.
| Payment Number | Balance start of month | Amount of Payment | Interest due, at end of month | Principal due, at end of month | Balance after Payment |
| 1 | $500 | $128.14 | $5 | $123.14 | $376.86 |
| 2 | $376.86 | $128.14 | $3.77 | $124.37 | $252.49 |
| 3 | $252.49 | $128.14 | $2.52 | $125.62 | $126.87 |
| 4 | $126.87 | $128.14 | $1.27 | $126.87 | $0 |
- A student buys a $2400 computer. The price will be amortized at 15% annual interest compounded monthly, and repaid in 6 substantially equal monthly payments.
- What monthly payment is required?
- b) Complete the amortization schedule below.
| Payment Number | Balance start of month | Amount of Payment | Interest due, at end of month | Principal due, at end of month | Balance after Payment |
| 1 | $2400 | $417.69 | $30 | $387.69 | $2012.69 |
| 2 | $2012.69 | $417.69 | $25.15 | $392.54 | $1619.77 |
| 3 | $1619.77 | $417.69 | $20.25 | $397.44 | $1222.33 |
| 4 | $1222.33 | $417.69 | $15.28 | $402.41 | $819.92 |
| 5 | $819.92 | $417.69 | $10.25 | $407.44 | $412.48 |
| 6 | $412.48 | $417.64 | $5.16 | $412.48 | $0 |
- How much did the student actually pay for the computer (starting balance + sum of interest column)?
- After using your computer for a year or so, you decide to upgrade to a better system. A friend buys your old computer for $750, and you use this for a down-payment on a new system that costs $4200. You finance the balance through the dealer in a sequence of nine substantially equal monthly payments, and the dealer charges 18% annual interest compounded monthly.
- What monthly payment is required?
- b) Complete the amortization schedule below.
| Payment Number | Balance start of month | Amount of Payment | Interest due, at end of month | Principal due, at end of month | Balance after Payment |
| 1 | $3450 | $412.66 | $51.75 | $360.91 | $3089.09 |
| 2 | $3089.09 | $412.66 | $46.34 | $366.32 | $2722.77 |
| 3 | $2722.77 | $412.66 | $40.84 | $371.82 | $2350.95 |
| 4 | $2350.95 | $412.66 | $35.26 | $377.40 | $1973.55 |
| 5 | $1973.55 | $412.66 | $29.60 | $383.06 | $1590.49 |
| 6 | $1590.49 | $412.66 | $23.86 | $388.80 | $1201.69 |
| 7 | $1201.69 | $412.66 | $18.03 | $394.63 | $807.06 |
| 8 | $807.06 | $412.66 | $12.11 | $400.55 | $406.51 |
| 9 | $406.51 | $412.61 | $6.10 | $406.51 | $0 |
How much did you actually pay for the computer (starting balance + sum of interest column + down payment)?
