PF: Chapter 7

What are the interest cost and the total amount due on a six-month loan of $1,500 at 13.2 percent simple annual interest? (Do not round your intermediate calculations. Round your answers to the nearest whole dollar.)

Interest =P × r × T = $1,500 × 0.132 × (6 / 12) = $99 Total amount due= Principal borrowed + Interest = $1,500 + 99 = $1,599

Rebecca wants to buy a new saddle for her horse. The one she wants usually costs $500, but this week it is on sale for $400. She does not have $400, but she could buy it with $50 down and pay the rest in 6 months with 10 percent interest. How much will Rebecca save by buying the saddle this week? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Interest =P × r × T = ($400 - 50) × 0.10 × (6 / 12) = $17.50 Total cost=Down payment + Principal borrowed + Interest = $50 + 350 + 17.50 = $417.50 Amount saved=Regular price - Total cost = $500 - 417.50 = $82.50

Sidney took a $200 cash advance by using checks linked to her credit card account. The bank charges a two percent cash advance fee on the amount borrowed and offers no grace period on cash advances. Sidney paid the balance in full when the bill arrived. (a) What was the cash advance fee? (b) What was the interest for one month at an 18 percent APR? (c) What was the total amount she paid?

A. Cash advance fee= Rate × Principal borrowed = 0.02 × $200 = $4 B. Interest= P × r × T = $200 × 0.18 × (1 / 12) = $3 C. Total repayment= Principal borrowed + Cash advance fee + Interest = $200 + 4 + 3 = $207

Dave borrowed $500 on January 1, 2006. The bank charged him a $5 service charge and interest was $50. If Dave paid the $500 in 12 equal monthly payments, what was the APR? (Enter your answer as a percent rounded to 1 decimal place.)

APR=(2 × n × I) / [P × (N + 1)] = (2 × 12 × $55) / [$500 × (12 + 1)] =$1,320 / $6,500 =0.203, or 20.3%

Dave borrowed $500 on January 1, 2006, and paid it all back at once on December 31, 2006. The bank charged him a $5 service charge and interest was $50.

Annual finance charge =Interest+Other costs = $50 + 5 = $55 APR=Annual finance charge / Principal borrowed = $55 / $500 = 0.11, or 11%

Dorothy lacks cash to pay for a $600 dishwasher. She could buy it from the store on credit by making 12 monthly payments of $52.74. The total cost would then be $632.88. Instead, Dorothy decides to deposit $50 a month in the bank until she has saved enough money to pay cash for the dishwasher. One year later, she has saved $642—$600 in deposits plus interest. When she goes back to the store, she finds that the dishwasher now costs $660. Its price has gone up 10 percent. Was postponing her purchase a good trade-off for Dorothy?

No

Bobby is trying to decide between two credit cards. One has no annual fee and an interest rate of 18 percent, and the other has a $40 annual fee and an interest rate of 8.9 percent. A) If Bobby pays his credit card balance in full each month, which card should he choose? B) If Bobby just pays the minimum payment and carries a balance from one month to the next, which card should he choose?

A) He should select the card without the annual fee. B) He should most likely select the card with the lowest interest rate

Dave borrowed $500 for one year and paid $50 in interest. The bank charged him a $5 service charge. What is the finance charge on this loan?

Finance charge = Interest + Other costs = $50 + 5 = $55

You can buy an item for $100 on a charge with the promise to pay $100 in 90 days. Suppose you can buy an identical item for $95 cash. If you buy the item for $100, you are in effect paying $5 for the use of $95 for three months. What is the effective annual rate of interest? Ignore interest rate compounding. (Do not round your intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

I=P × r × T $5 = $95 × r × 3/12 $5 = $23.75r r = $5 / $23.75 r = 0.2105, or 21.05%

After visiting several automobile dealerships, Richard selects the used car he wants. He likes its $10,000 price, but financing through the dealer is no bargain. He has $2,000 cash for a down payment, so he needs an $8,000 loan. In shopping at several banks for an installment loan, he learns that interest on most automobile loans is quoted at add-on rates. That is, during the life of the loan, interest is paid on the full amount borrowed even though a portion of the principal has been paid back. Richard borrows $8,000 for a period of four years at an add-on interest rate of 11 percent. A) What is the total interest on Richard's loan? (Do not round your intermediate calculations. Round your answer to the nearest whole dollar.) B) What is the total cost of the car? (Do not round your intermediate calculations. Round your answer to the nearest whole dollar.) C) What is the monthly payment? (Do not round your intermediate calculations. Round your answer to the nearest whole dollar.) D) What is the annual percentage rate (APR)? (Do not round your intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

A) Interest=P × r × T = $8,000 × 0.11 × 4 = $3,520 B) Total cost=Down payment + Total interest + Principal = $2,000 + 3,520 + 8,000 = $13,520 C) Monthly payment= (Principal borrowed + Total interest) / Total number of payments = ($8,000 + 3,520) / 48 = $240 D) APR=(2 × n × I) / [P × (N + 1)] = (2 × 12 × $3,520) / [$8,000 × (48 + 1)] = $84,480 / $392,000 = 0.2155, or 21.55%

Your uncle lends you $2,000 less $100 (interest at 5 percent), and you receive $1,900. The loan is for one year and will be repaid in one lump sum at the end of the year. Use the APR formula to find the true annual percentage rate. (Enter your answer as a percent rounded to 3 decimal places.)

APR=(2 × n × I) / [P × (N + 1)] = (2 × 1 × $100) / [$1,900 × (1 + 1)] = 0.05263, or 5.263%

Damon convinced his aunt to lend him $2,000 to purchase a plasma digital TV. She has agreed to charge only 6 percent simple interest, and he has agreed to repay the loan at the end of one year. How much interest will he pay for the year?

I=P × r × T = $2,000 × 0.06 × 1 = $120

You have been pricing a compact disk player in several stores. Three stores have the identical price of $300. Each store charges 18 percent APR, has a 30-day grace period, and sends out bills on the first of the month. On further investigation, you find that store A calculates the finance charge by using the average daily balance method, store B uses the adjusted balance method, and store C uses the previous balance method. Assume you purchased the disk player on May 5 and made a $100 payment on June 15. What will the finance charge be (for June) if you made your purchase from store A? From store B? From store C? (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

Store A. Finance charge for June =[Beginning balance + Ending balance) / 2] × (Annual interest rate / 12) = [($300 + 200) / 2] × (0.18 / 12) = $3.75 Store B. Finance charge for June =(Beginning balance - Payments) × (Annual interest rate / 12) = ($300 - 100) × (0.18 / 12) = $3.00 Store C. Finance charge for June =Beginning balance × (Annual interest rate / 12) = $300 × (0.18 / 12) = $4.50