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Exam 4: Time Value of Money

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Question 31

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Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?

A) $2,404.91
B) $2,531.49
C) $2,658.06
D) $2,790.96
E) $2,930.51

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

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Question 32

Multiple Choice

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Your father's employer was just acquired, and he was given a severance payment of $375,000, which he invested at a 7.5% annual rate. He now plans to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. What is the maximum number of whole payments that can be withdrawn before the account is exhausted; i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

A) 22
B) 23
C) 24
D) 25
E) 26

F) A) and E)
G) None of the above

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Question 33

Multiple Choice

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Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years.

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account?

You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%?

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. What is the maximum number of $45,000 withdrawals that she can make and still have at least $50,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

Your bank offers to lend you $100,000 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?

If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.

Which of the following statements is CORRECT?

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?

Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12) . The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0) . If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?