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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.

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