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Quoting Rates

54. Quoting Rates. Banks sometimes quote interest rates in the form of ¬add-on interest. ­ In this case, if a 1-year loan is quoted with a 20 percent interest rate and you borrow $1,000, then you pay back $1,200. But you make these payments in monthly installments of $100 each. What are the true APR and effective annual rate on this loan? Why should you have known that the true rates must be greater than 20 percent even before doing anycalculations?

55. Compound Interest. Suppose you take out a $1,000, 3-year loan using add-on interest (see previous problem) with a quoted interest rate of 20 percent per year. What will your monthly payments be? (Total payments are $1,000 + $1,000 .20 3 = $1,600.) What are the true APR and effective annual rate on this loan? Are they the same as in the previous problem?

56. Calculating Interest Rate. What is the effective annual rate on a one-year loan with an interest rate quoted on a discount basis (see problem 25) of 20 percent?

57. Effective Rates. First National Bank pays 6.2 percent interest compounded semiannually. Second National Bank pays 6 percent interest, compounded monthly. Which bank offers the higher effective annual rate?

58. Calculating Interest Rate. You borrow $1,000 from the bank and agree to repay the loan over the next year in 12 equal monthly payments of $90. However, the bank also charges you a loan-initiation fee of $20, which is taken out of the initial proceeds of the loan. What is the

effective annual interest rate on the loan taking account of the impact of the initiation fee?

59. Retirement Savings. You believe you will need to have saved $500,000 by the time you retire in 40 years in order to live comfortably. If the interest rate is 5 percent per year, how much must you save each year to meet your retirement goal?

60. Retirement Savings. How much would you need in the previous problem if you believe that you will inherit $100,000 in 10 years?

61. Retirement Savings. You believe you will spend $40,000 a year for 20 years once you retire in 40 years. If the interest rate is 5 percent per year, how much must you save each year until retirement to meet your retirement goal?

62. Retirement Planning. A couple thinking about retirement decide to put aside $3,000 each year in a savings plan that earns 8 percent interest. In 5 years they will receive a gift of $10,000 that also can be invested.

a. How much money will they have accumulated 30 years from now?

b. If their goal is to retire with $800,000 of savings, how much extra do they need to save every year?

63. Retirement Planning. A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last about 25 years. They believe that they can earn 10 percent interest on retirement savings.

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year.

b. How would the answer to part (a) change if the couple also realize that in 20 years, they will need to spend $60,000 on their child`s college education?