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Exam 5: Time Value of Money

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Question 1

True/False

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The present value of a future sum decreases as either the discount rate or the number of periods per year increases,other things held constant.

A) True
B) False

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Question 2

Multiple Choice

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Sam was injured in an accident,and the insurance company has offered him the choice of $46,000 per year for 15 years,with the first payment being made today,or a lump sum.If a fair return is 7.5%,how large must the lump sum be to leave him as well off financially as with the annuity?

A) $536,896.32
B) $475,786.17
C) $541,261.33
D) $453,961.11
E) $436,501.07

F) A) and E)
G) B) and C)

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Question 3

Multiple Choice

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Your bank account pays an 8% nominal rate of interest.The interest is compounded quarterly.Which of the following statements is CORRECT?

You plan to invest some money in a bank account.Which of the following banks provides you with the highest effective rate of interest?

A U.S.Treasury bond will pay a lump sum of $1,000 exactly 3 years from today.The nominal interest rate is 6%,semiannual compounding.Which of the following statements is CORRECT?

Which of the following statements is CORRECT,assuming positive interest rates and holding other things constant?

As a result of compounding,the effective annual rate on a bank deposit (or a loan)is always equal to or less than the nominal rate on the deposit (or loan).

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $170.00 at the end of each quarter and then pay off the principal amount at the end of the year.What is the effective annual rate on the loan?

As a result of compounding,the effective annual rate on a bank deposit (or a loan)is always equal to or greater than the nominal rate on the deposit (or loan).

Suppose Sally Smith plans to invest $1,000.She can earn an effective annual rate of 5% on Security A,while Security B has an effective annual rate of 12%.After 11 years,the compounded value of Security B should be more than twice the compounded value of Security A.(Ignore risk,and assume that compounding occurs annually. )

The greater the number of compounding periods within a year,then (1)the greater the future value of a lump sum investment at Time 0 and (2)the smaller the present value of a given lump sum to be received at some future date.

You are offered a chance to buy an asset for $4,500 that is expected to produce cash flows of $750 at the end of Year 1,$1,000 at the end of Year 2,$850 at the end of Year 3,and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

Suppose you deposited $27,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year.How much would be in the account after 8 months,assuming each month has 30 days?

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%,compounded monthly.If you invest $5,000 at the beginning of each month,how many months would it take for your account to grow to $280,000? Round fractional months up.

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

Your bank offers to lend you $113,200 at an 8.5% annual interest rate to start your new business.The terms require you to amortize the loan with 10 equal end-of-year payments.How much interest would you be paying in Year 2?

Janice has $5,000 invested in a bank that pays 8.4% annually.How long will it take for her funds to triple?

What is the PV of an annuity due with 5 payments of $2,900 at an interest rate of 5.5%?

Your brother's business obtained a 30-year amortized mortgage loan for $125,000 at a nominal annual rate of 7.0%,with 360 end-of-month payments.The firm can deduct the interest paid for tax purposes.What will the interest tax deduction be for Year 1?

You just deposited $6,500 in a bank account that pays a 4.0% nominal interest rate,compounded quarterly.If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now,how much will be in the account three years (12 quarters) from now?