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Financial Algebra

Robert Gerver, Richard Sgroi

Chapter 4

Consumer Credit

Educators


Problem 1

Interpret the quote in the context of what you learned.

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Problem 2

Monique buys a $\$ 4,700$ air conditioning system using an installment plan that requires 15$\%$ down. How much is the down payment?

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Problem 3

Craig wants to purchase a boat that costs $\$ 1,420 .$ He signs an installment agreement requiring a 20$\%$ down payment. He currently has $\$ 250$ saved. Does he have enough for the down payment?

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Problem 4

Jean bought a $\$ 1,980$ snow thrower on the installment plan. The installment agreement included a 10$\%$ down payment and 18 monthly payments of $\$ 116$ each.
a. How much is the down payment?
b. What is the total amount of the monthly payments?
c. How much did Jean pay for the snow thrower on the installment plan?
d. What is the fi nance charge?

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Problem 5

Linda bought a washer and dryer from Millpage Laundry Supplies for $y$ dollars. She signed an installment agreement requiring a 15$\%$ down payment and monthly payments of $x$ dollars for one year.
a. Express her down payment algebraically.
b. How many monthly payments must Linda make?
c. Express the total amount of the monthly payments algebraically.
d. Express the total amount Linda pays for the washer and dryer on the installment plan algebraically.
e. Express the fi nance charge algebraically.

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Problem 6

Zeke bought a $\$ 2,300$ bobsled on the installment plan. He made a $\$ 450$ down payment, and he has to make monthly payments of $\$ 93.50$ for the next two years. How much interest will he pay?

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Problem 7

Gary is buying a $\$ 1,250$ computer on the installment plan. He makes a down payment of $\$ 150 .$ He has to make monthly payments of $\$ 48.25$ for 2$\frac{1}{2}$ years. What is the finance charge?

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Problem 8

Mazzeo's Appliance Store requires a down payment of $\frac{1}{3}$ on all installment purchases. Norton's Depot requires a 30$\%$ down payment on installment purchases. Which store's down payment rate is lower?

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Problem 9

Ari purchased a microwave oven on the installment plan for $m$ dollars. He made a 20$\%$ down payment and agreed to pay $x$ dollars per month for the two years. Express the finance charge algebraically.

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Problem 10

Adam bought a $\$ 1,670$ custom video game/sound system on a special no-interest plan. He made a $\$ 100$ down payment and agreed to pay the entire purchase off in 1$\frac{1}{2}$ years. The minimum monthly payment is $\$ 10 .$ If he makes the minimum monthly payment up until the last payment, what will be the amount of his last payment?

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Problem 11

Max created a spreadsheet for installment purchase calculations.
a. Write a spreadsheet formula to compute the down payment in cell C2.
b. Write a spreadsheet formula to compute the time in months in cell F2.
c. Write a spreadsheet formula to compute the total of monthly payments in cell G2.
d. Write the spreadsheet formula to compute the fi nance charge in cell H2.
e. Use your answers to a–d to fi ll in the missing entries f–v.

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Problem 12

A layaway plan is similar to an installment plan, but the customer does not receive the merchandise until it is paid for. It is held in the store for a fee. If you purchased a $\$ 1,700$ set of golf clubs on a nine-month layaway plan and had to pay a monthly payment of $\$ 201$ , what is the sum of the monthly payments? What was the fee charged for the layaway plan?

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Problem 13

A deferred payment plan is also similar to an installment plan, except there are very low monthly payments until the end of the agreement. At that point, the entire purchase must be paid in full. If it is not paid, there will be high finance charges. Often, there is no interest-stores use no-interest deferred payment plans to attract customers. Many times there is also no down payment.
a. Chris purchases a living room furniture set for $\$ 4,345$ from Halloran Gallery. She has a one-year, no interest, no money down, deferred payment plan. She does have to make a $\$ 15$ monthly payment for the first 11 months. What is the sum of these monthly payments?
b. How much must Chris pay in the last month of this plan?
c. What is the difference between the layaway plan in Exercise 12 and the deferred payment plan?

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Problem 14

Audrey purchases a riding lawnmower using the 2 -year no-interest deferred payment plan at Lawn Depot for $x$ dollars. There was a down payment of $d$ dollars and a monthly payment of $m$ dollars. Express the amount of the last payment algebraically.

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Problem 15

Some stores offer a rent-to-own plan. The customer makes a down payment, receives the merchandise at time of purchase, and makes monthly payments. The sum of the monthly payments is lower than the cost of the item. When the last payment is made, customers make a choice. They can purchase the item and apply their payments towards the cost. They can return the item, which means they rented it for a certain period of months.
a. Sharon bought a $\$ 2,100$ high-definition television set (HDTV) on a six-month rent-to-own plan. The down payment? What was the dollar value of the down payment?
b. Her monthly payments were $\$ 75$ per month. If she decides not to buy the HDTV after the six months, what was her cost to rent it?

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Problem 16

Bernie bought a refrigerator at a special sale. The refrigerator regularly sold for $\$ 986 .$ No down payment was required. Bernie has to pay $\$ 69$ for the 1$\frac{1}{2}$ years. What is the average amount Bernie pays in interest each month?

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Problem 17

Lillian purchased a guitar from Smash Music Stores. It regularly sold for $\$ 670$ , but was on sale at 10$\%$ off. She paid 8$\%$ tax. She bought it on the installment plan and paid 15$\%$ of the total cost with tax as a down payment. Her monthly payments were $\$ 58$ per month for one year.
a. What is the discount?
b. What is the sale price?
c. What is the sales tax?
d. What is the total cost of the guitar?
e. What is the down payment?
f. What is the total of the monthly payments?
g. What is the total she paid for the guitar on the installment plan?
h. What is the fi nance charge?

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Problem 18

The following inequalities give information on your credit scores. Let $x$ represent your credit score.
$\bullet$ If $x>700,$ your credit score is excellent.
$\bullet$ If $680< x< 700,$ your credit score is good.
$\bullet$ If $620< x< 680$ , your credit score should be watched carefully.
$\bullet$ If $580< x< 620$ , your credit score is low
$\bullet$ If $x< 580,$ your credit score is poor.
If Mary Ann's credit score is low, but she receives 40 points for paying off some delinquent debts, is it possible that her credit rating is now good? Explain.

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Problem 19

Samantha's grandfather is debt-free-he bought his car and his house without taking out a loan. He saved and paid cash. He wanted to take out a loan to buy Samantha a car for college graduation. The bank turned him down. Explain why.

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Problem 20

Bianka has a credit line of $\$ 8,000 .$ She had a previous balance of $\$ 567.91$ and made a payment of $\$ 1,200 .$ Her total purchases are $\$ 986.79,$ and she has been charged a $\$ 10.00$ finance charge. What is her available credit?

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