-------136 MORE INTERESTFORMULASthe principal. What is the nominal annual interest rate 4-68 A student bought a $75 used guitar and agreed to pa:
that, they are charging? for it with a single $85 payment at the end of 6 months
4-59 What effective interest rate per annum corresponds Assuming semiannual (every 6 months) compound
to a nominal rate of 12% compounded monthly? ing, what is the nominal annual interest rate? What i:
(Answer: 12.7%) the effective interest rate?
4-60 A woman opened an account in a local store. In 4-69 A firm charges its credit customers 13/4%interest pe
the charge account agreement, the store indicated it month. What is the effective interest rate?
charges 11/2% each month on the unpaid balance. 4-70 A thousand dollars is invested for 7 months at at
What nominal annual interest rate is being charged? interest rate of 1%. per month. What is the nomi
What is the effective interest rate? nal interest rate? What is the effective interest rate'
4-61 TheBawl Street Journal costs $206, payable now, (Answers: 12%; 12.7%)
for a 2-year subscription. The newspaper is published 4-71 What interest rate, compounded quarterly, is equiva.
252 days per year (5 days per week, except holidays). lent to a 9.31 % effective interest rate?
If a 10% nominal annual interest rate, compounded 4-72 If the nominal annual interest rate is 12% com
.quarterly,is used: pounded quarterly, what is the effective annual in.
(a)What is the effective annual interest rate in this terest rate?
problem? 4-73
(b) Compute the equivalent interest rate per 1/252of A contractor wishes to set up a special fund by male.
a year. 'ing uniform semiannual end-of-period deposits fo]
(c)What is a subscriber's cost per copy of the news- 20 years. The fund is to provide $10,000 at the enc
paper, taking interest into account? of each of the last 5 years of the 20-year period. 1.1.
4-62 interest is 8%, compounded semiannually, what is the
Pete Sampras borrows $10,000 to purchase a car. He required semiannual deposit?
must repay the loan in 48 equal end-of-period monthly 4-74
payments. Interest is calculated at 1.25% per month. What amount will be reqUired to pur<?hase,on a man'
Determine the following: 40th birthday, an annuity to provide him with 30 equaJ
(a) The nominal annual interest rate semiannual payments of $1000 each, the first to be
(b) The effective annual interest rate received on his 50th birthday, if nominal hiterest i
(c)The amount of the monthly payment 4% compounded semiannually?
4-63 Picabo Street borrows $1000. To repay the amount she 4-75 A man decides to deposit $50 in the bank today and
makes 12 equal monthly payments of $90.30. Deter- to make 10 additional deposits every 6 months begin-
mine the following: ning 6 months from now, the first of which will be
(a)The effective monthly interest rate $50 and increasing $10 per deposit after that. A few
(b)The nominal annual interest rate minutes after making the last deposit, he decides to
(c) The effective annual interest rate withdraw all the money deposited. If the bank pays
4-64 .6% nominal interest compoUnded semiannually, how
At the Central Furniture Company, customers who much money will he receive?
purchase on credit pay an effective annual interest rate 4-76
of 16.1%, based on monthly compounding. What is A man makes an investment every 3 months at a
the nominal annual interest rate that they pay? nominal annual interest rate of 28%, compounded
quarterly. His first investment was $100, followed
4-65 What monthly interest rate is equivalent to an effec- by investments increasing$20 each 3 months. Thus,
tive annual interest rate of 18%? the second investment was $120, the third investment
4-66 A bank advertises it pays 7% annual interest, com- $140, and so on. If he continues to make this series of
pounded daily, on savings accounts, provided the investments for a total of 20 years, what will be the
money is left in the account for 4 years. What value of the investments at the end of that time?
effective annual interest rate do they pay? 4-77 A 25-year old engineer is opening an individual retire-
4-67 To repay a $1000 loan, a man paid $91.70 at the end ment account (IRA) at a bank. Her goal is to accwnu-
of each month for 12 months. Compute the nominal late $1 million in the account by the time she retires
interest rate he paid. from work in 40 years. The bank manager estimates