Chapter 7 Problems
Your uncle lends you $9,200 less $552 (interest at 6 percent), and you receive $8,648. Use the APR formula to find the true annual percentage rate. Assume you repay the entire loan in one year. (Enter your answer as a percent rounded to 3 decimal places.)
- APR= (2 × n × I) / [P × (N + 1)] - APR = (2 × 1 × 552) / [8648 × (1+1)] = 21.55%
Dave borrowed $550 on January 1, 2017. The bank charged him a service charge of $7.00 and interest was $45.25. If Dave paid the $550 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)] - APR = (2 × 12 × 55) / [500 × (12 + 1)] = 20.3%
Dave borrowed $500 on January 1, 2017, and paid it all back at once on December 31, 2017. The bank charged him a service charge of $5 and interest was $50. What was the APR? (Enter your answer as a percent rounded to the nearest whole number.)
- Annual Finance Charge = Interest + Other Costs - Annual Finance Charge = 50 + 5 = 55 - APR= Annual Finance Charge / Principal Borrowed - APR = 55 / 500 = 11%
Sidney took a cash advance of $200 by using checks linked to her credit card account. The bank charges a cash advance fee of 2 percent on the amount borrowed and offers no grace period on cash advances. Sidney paid the balance in full when the bill arrived. What was the interest for one month at an APR of 18 percent? What was the total amount she paid?
- Cash Advance Fee = Rate × Principal Borrowed - Cash Advance Fee = .02 × 200 = 4 - I = Prt - I = (200)(.18)(1/12) = 3 - Total Repayment = Principal Borrowed + Cash Advance Fee + Interest - Total Repayment = 200 + 4 + 3 = 207
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 intermediate calculations. Round your answers to the nearest whole number.)
- I = Prt - I = (1500)(.132)(6/12) = 99 - Total Cost = Down Payment + Principal Borrowed + Interest - Total Cost = 0 + 1500 + 99 = 1599
Damon convinced his aunt to lend him $3,700 to purchase a plasma digital TV. She has agreed to charge only 9 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 = Prt - I = (3700)(.09)(1) = 333
Rebecca wants to buy a new saddle for her horse. The one she wants usually costs $550, but this week it is on sale for $470. She does not have $470, but she could buy it with $50 down and pay the rest in 6 months with 8 percent interest. Does Rebecca save any money buying the saddle this way? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
- I = Prt - I = (470-50)(.08)(6/12) = 16.8 - Total Cost = Down Payment + Principal Borrowed + Interest - Total Cost = 50 + 420 + 16.8 = 486.8 - Amount Saved = Regular Price - Total Cost - Amount Saved = 550 - 486.8 = 63.2
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 a loan of $8,000. 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. What is the total interest on Richard's loan? (Do not round intermediate calculations. Round your answer to the nearest whole number.) What is the total cost of the car? (Do not round intermediate calculations. Round your answer to the nearest whole number.) What is the monthly payment? (Do not round intermediate calculations. Round your answer to the nearest whole number.) What is the annual percentage rate (APR)? (Do not round your intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
- I = Prt - I = (8000)(.11)(4) = 3520 - Total Cost = Down Payment + Principal Borrowed + Interest - Total Cost = 2000 + 8000 + 3520 = 13520 - Monthly Payment = (Principal Borrowed + Total interest) / Total number of payments - Monthly Payment = (8000 + 3520) / 48 - APR= (2 × n × I) / [P × (N + 1)] - APR = (2 × 12 × 3520) / [8000 × (48+1)] = 21.55%
