u_......_.. ... ... ..- -...-.- - -- --- .- -_. --- ---
r138 MORE INTERESTFORMULASend of 2 months, the total interest charged (a) What was his monthly loan payment?
ould be (12 + 11)/78, or 23/78 of the (b) What must he have paid (in addition to his regu-
year's interest. After 11 months the inter- lar 120th monthly payment) to pay the remaining
est charge would therefore be 77/78 of the balance of his loan?
total year's interest. (c)Recomputepart(a) using 6% compounded
continuously.
Helen.Reddy borrowed $10,000 on January 1 at 9%
annual interest, compounded monthly. The loan was 4-93 An automobile may be purchased with a $3000 down
to be repaid in 12 equal end-of-period payments. payment now and 60 ,monthly payments of $280. If
Helen made the first two payments and then decided the interest rate is 12% compounded monthly, what
to repay the balance of the loan when she pays the is the price of the automobile?
third payment. Thus she will pay the third payment 4-94 A man has $5000 on deposit in a bank that pays 5%
plus an additional sum. interest compounded annually. He wonders how
You are to calculate the amount of this additional much more advantageous it would be to transfer his
sum funds to another bank whose dividend policy is 5%
(a) Based on the rule of 78s. interest, compounded continuously. Compute how
(b) Based on exact economicanalysis methods. much he would have in his savings account at the
4-89 Abankis offering a loan of $25,000 with a nominal end of 3 years under each of these situations.
interest rate of 18% compounded monthly, payable 4-95 A friend was left $50,000 by his uncle. He has de-
in 60 months.(Hint:The loan origination fee of 2% cided to put it into a savings account for the next
will be taken out from the loan amount.) year or so. He finds there are varying interest rates
(a)Whatis the monthlypayment? at savings institutions: 43/8% compounded annually,
(b)If a loan origination fee of 2% is charged at the 41/4% compounded quarterly, and 41/8%compounded
time of the loan, what is the effective interest rate? continuously. He wishes to select the savings institu-
4-90 Our cat, Fred, wants to purchase a new litter box. The tion that will give him the highest return on his money.
cost is $100 and he'll finance it over 2 years at an What interest rate should he select?
annual rate of 18% compounded monthly and to be 4-96 One of the local banks indicates that it computes the
repaid in 24 monthly payments. interest it pays on savings accounts by the continuous
(a)What is his monthlypayment? compounding method. Suppose you deposited $100
(b)At the time of the thirteenth payment, Fred in the bank and they pay 4% per annum, compounded
decides to payoff the remainder of the loan. continuously. After 5 years, how much money will
Using regular compound interest factors, determine there be in the account?
the amount of this last payment. 4-97 A college professor won $85,000 in the state lot-4-91 Our cat, Fred, has convinced me that I should set up tery; income taxes will take about half the amount.
an account that will assure him of his Meow Mix for She plans to spend her sabbatical year on leave from
the next 4 years. I will deposit an amount Ptoday the university on an around-the-world trip with her
that will permit Fred to make end-of-the-month with- husband, but she must continue to teach 3 more years
drawals of $10 for the next 48. months. Consider an first. She estimates the trip will cost $40,000 and they
interest rate of 6% compounded monthly and that the will spend the money as a continuous flow of funds
account will be emptied with the last withdrawal. during their year of travel. She will put nough of her
(a)What is the value ofPthat I must deposit today? lottery winnings in a bank account now to pay for
(b) What is the account balance immediately after the trip. The bank pays7%nominal interest, com-
the 24th withdrawal has been made? pounded continuously. She asks you to compute how
4-92 When Jerry Garcia was alive he bought a house for much she should set aside in the account for the
$500,000 and made a $100,000 down payment. He trip.
obtained a 30-year loan for the remaining amount. 4-98 Michael Jacks deposited $500,000 into a bank for
Payments were made monthly. The nominal annual 6 months. At the end of that time, he withdrew the
interest rate was 9%. After 10 years (120 payments) money and received $520,000. If the bank paid inter-
he decided to pay the remaining balance on the loan. est based on continuous compounding: