# Interest and the Time Value of Money

Please help with the following:

Section 5.1

36, 40, 46, 52

Section 5.2

20, 38, 44, 52, 58, 68

Section 5.3

22, 34, 40

36. Stock Growth A stock that sold for $22 at the beginning of

the year was selling for $24 at the end of the year. If the

stock paid a dividend of $.50 per share, what is the simple

interest rate on an investment in this stock? (Hint: Consider

the interest to be the increase in value plus the dividend.)

40. Loan Interest A developer needs $80,000 to buy land. He

is able to borrow the money at 10% per year compounded

quarterly. How much will the interest amount to if he pays

off the loan in 5 years?

46. Effective Rate An advertisement for E*TRADE Bank

boasted "We're ahead of banks that had a 160-year start,"

with an APY (or effective rate) of 2.01%.* The actual rate

was not stated. Given that interest was compounded

monthly, find the actual rate.

52. Doubling Time Suppose a conservation campaign coupled

with higher rates causes the demand for electricity to

increase at only 2% per year, as it has recently. Find the

number of years before the utilities will need to double

generating capacity

20. Explain the difference between an ordinary annuity and an annuity due.

Find the future value of each annuity due.

38. $1500 deposited at the beginning of each semiannual period for 11 years at 5.6% compounded semiannually

Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the following amounts.

Payments are made at the end of each period.

44. $75,000; money earns 6% compounded semiannually for 4 ½ years

52. Savings A father opened a savings account for his daughter

on the day she was born, depositing $1000. Each year on her

birthday he deposits another $1000, making the last deposit

on her twenty-first birthday. If the account pays 9.5% interest

compounded annually, how much is in the account at the

end of the day on the daughter's twenty-first birthday?

58. Buying Equipment Harv, the owner of Harv's Meats,

knows that he must buy a new deboner machine in 4 years.

The machine costs $12,000. In order to accumulate enough

money to pay for the machine, Harv decides to deposit a

sum of money at the end of each 6 months in an account

paying 6% compounded semiannually. How much should

each payment be?

68. Buying Rare Stamps Paul Altier bought a rare stamp for

his collection. He agreed to pay a lump sum of $4000 after

5 years. Until then, he pays 6% simple interest semiannually

on the $4000.

Find the payment necessary to amortize each loan.

22. $5500; 12.5% compounded monthly; 24 monthly payments

34. Installment Buying Stereo Shack sells a stereo system

for $600 down and monthly payments of $30 for the next

3 years. If the interest rate is 1.25% per month on the

unpaid balance, find

a. the cost of the stereo system;

b. the total amount of interest paid.

Student Loans Student borrowers now have more options to

choose from when selecting repayment plans.* The standard

plan repays the loan in 10 years with equal monthly payments.

The extended plan allows from 12 to 30 years to repay the loan.

A student borrows $35,000 at 7.43% compounded monthly.

40. Find the monthly payment and total interest paid under the

standard plan.