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Exam 14: Time Value of Money

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Question 31

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Paul wants to invest a sum of money today that will accumulate to $50,000 at the end of 4 years. Assuming he can earn an interest rate of 8% compounded semiannually, how much must he invest today? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

A) $36,535
B) $27,015
C) $42,740
D) $36,750
E) $31,414

F) A) and B)
G) A) and D)

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Question 32

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A company borrows money from the bank by promising to make 6 annual year-end payments of $27,000 each. How much is the company able to borrow if the interest rate is 9%?

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Question 33

Multiple Choice

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Jessica received a gift of $7,500 at the time of her high school graduation. She invests it in an account that yields 10% compounded semiannually. What will the value of Jessica's investment be at the end of 5 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

A company has $46,000 today to invest in a fund that will earn 4% compounded annually. How much will the fund contain at the end of 6 years?

A company is beginning a savings plan to purchase a new building. It will be saving $43,000 per year for the next 10 years. How much will the company have accumulated after the tenth year-end deposit, assuming the fund earns 9% interest?

Explain the concept of the future value of a single amount.

A series of equal payments made or received at the end of each period is an ordinary annuity.

A company needs to have $200,000 in 4 years, and will create a fund to insure that the $200,000 will be available. If it can earn a 7% return compounded annually, how much must the company invest in the fund today to equal the $200,000 at the end of 4 years?

When you reach retirement age, you will have one fund of $100,000 from which you are going to make annual withdrawals of $14,702. The fund will earn 6% per year. For how many years will you be able to draw an even amount of $14,702?

Sandra has a savings account that has accumulated to $50,000. She started with $28,225, and earned interest at 10% compounded annually. It took her five years to accumulate the $50,000. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Trey has $105,000 now. He has a loan of $175,000 that he must pay at the end of 5 years. He can invest his $105,000 at 10% interest compounded semiannually. Will Trey have enough to pay his loan at the end of the 5 years?

Explain the concept of the future value of an annuity.

Pelcher Company acquires a machine by issuing a note that requires semiannual payments of $4,000 for 3 years. The interest rate on the note is 10% compounded semiannually. What is the cost of the machine? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

With deposits of $5,000 at the end of each year, you will have accumulated $38,578 at the end of the sixth year if the annual rate of interest is 10%. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

An individual is planning to set-up an education fund for her daughter. She plans to invest $7,000 annually at the end of each year. She expects to withdraw money from the fund at the end of 9 years and expects to earn an annual return of 8%. What will be the total value of the fund at the end of 9 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

How long will it take an investment of $25,000 at 6% compounded annually to accumulate to a total of $35,462.50? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

The future value of an ________ annuity is the accumulated value of each annuity payment with interest as of the date of the final payment.

Cody invests $1,800 per year from his summer wages at a 4% annual interest rate. He plans to take a European vacation at the end of 4 years when he graduates from college. How much will he have available to spend on his vacation? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Giuliani Co. lends $524,210 to Craig Corporation. The terms of the loan require that Craig make six semiannual period-end payments of $100,000 each. What semiannual interest rate is Craig paying on the loan?

Define interest.