654 CHAPTER 10 Consumer Mathematics c) If, after the 5-year initial rate period, the rate of the one-year Treasury bill rises to 2.5% determine the Cunninghams’ new ARM rate. 6.0% 10.6 43. Vacation Savings To save money to take an around- theworld vacation, Kim invests $250 monthly in an ordinary annuity with a 9% interest rate compounded monthly. Determine the accumulated amount in Kim’s annuity after 10 years. $48,378.57 44. Saving for a New Boat Raja would like to save $80,000 to buy a new Chris Craft Silver Bullet boat in 5 years. To accumulate $80,000 in 5 years, how much should Raja invest quarterly in a sinking fund with a 3.6% interest rate compounded quarterly? $3668.72 Test CHAPTER 10 1. Determine the missing quantity by using the simple Interest formula. a) p r t i $1600, 2.7%, 27 months, ? = = = = $97.20 b) p r t i $4200, 3.2%, ?, $268.80 = = = = 2 years In Exercises 2 and 3, Patty borrowed $1900 from a bank for 18 months to buy a new office computer. The simple interest rate charged is 3.15%. 2. How much interest did Patty pay for the use of the money? $89.78 3. What is the amount Patty repaid to the bank on the due date of the loan? $1989.78 In Exercises 4 and 5, Yolanda received a $5400 loan with a 12.5% interest rate for 90 days on August 1. Yolanda made a payment of $3000 on September 15. 4. How much did she owe the bank on the maturity date? $2523.20 5. What total amount of interest did she pay on the loan? $123.20 6. Use the compound interest formula to compute the accumulated amount and the interest earned. Principal Time Rate Compounded a) $7500 2 years 3% Quarterly b) $2500 3 years 6.5% Monthly a) $7961.99; $461.99 b) $3036.68; $536.68 A New Bicycle In Exercises 7–9, Don purchases a new bicycle that sells for $2350 using a bank loan. To finance the loan the bank will require a down payment of 15% and monthly payments of $90.79 for 24 months. 7. How much money will Don borrow from the bank? $1997.50 8. What finance charge will Don pay the bank? $181.46 9. What is the APR? 8.5% 10. Actuarial Method Gino borrowed $7500. To repay the loan, he was scheduled to make 36 monthly installment payments of $223.10. Instead of making his 24th payment, Gino decides to pay off the loan. a) Determine the APR of the installment loan. 4.5% b) How much interest will Gino save (use the actuarial method)? $64.13 c) What is the total amount due to pay off the loan? $2836.17 11. Previous Balance Method Michael’s credit card statement shows a balance due of $878.25 on March 23, the billing date. For the period ending on April 23, he had the following transactions. March 26 Charge: Groceries $95.89 March 30 Charge: Restaurant bill 68.76 April 3 Payment 450.00 April 15 Charge: Clothing 90.52 April 22 Charge: Eyeglasses 450.85 a) Determine the finance charge on March 23 by using the previous balance method. Assume that the interest rate is 1.4% per month. $12.30 b) Determine the new account balance on April 23 using the finance charge found in part (a). $1146.57 c) Determine the average daily balance for the period. $765.67 d) Determine the finance charge on April 23 by using the average daily balance method. Assume that the interest rate is 1.4% per month. $10.72 e) Determine the new account balance on April 23 using the finance charge found in part (d). $1144.99 Building a House In Exercises 12–18, the Leungs decided to build a new house. The contractor quoted them a price of $215,000, including the lot. The taxes on the house would be $3200 per year, and homeowners’ insurance would cost $450 per year. They have applied for a conventional loan from a bank. The bank is requiring a 15% down payment, and the interest rate is 5.5% with 2 points. The Leung’s annual income is $122,740. They have more than 10 monthly payments remaining on each of the following: $220 for
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