Exam 7: Accounting and the Time Value of Money
List the variables in a single-sum problem.
1. Present value of single sum
2. Future value of single sum
3. Interest rate per compounding period
4. Time period or number of compounding periods
You are provided with two-time value of money tables. One table provides factors for the present value of an ordinary annuity and the other provides factors for the present value of an annuity due. How can you tell which table is which type?
An ordinary annuity is an annuity where the cash flows occur at the end of the interest period and an annuity due is an annuity where the cash flows occur at the beginning of the interest period.
Therefore, for any given number of periods, and a set interest rate, the present value factor for an ordinary annuity is always smaller than the corresponding present value factor for an annuity due. For the first period, the present value factor for an annuity due is always 1.0 for any interest rate while the present value factor for an ordinary annuity is always less than one (one divided by one plus the interest rate).
Punjab Company borrowed $114,000 from its bank. Punjab will repay $140,000 in 7 years. What is the approximate interest rate that Punjab will incur on this loan, assuming annual compounding? Use a financial calculator or a spreadsheet to derive your answer. (Do not round any intermediary calculations, and round your final answer two decimal places, X.XX%.)
B
Explain how to determine the present value for any deferred, ordinary annuity by using only the table for factors of the present value of an ordinary annuity.
What is the market price of a $400,000, ten-year, 5% bond issue sold to yield an effective rate of 3% if interest is paid semiannually? (Use spreadsheet software or a financial calculator to calculate your answer. Do not round any intermediary calculations, and round your final answer to the nearest dollar.)
Each quarter for the next 10 years, Carmen Lector will deposit $1,000 into an investment fund that pays 8% compounded quarterly. Use the following tables:
Excerpt from the Present Value of an Ordinary Annuity of $1 Table
Periods 2\% 4\% 6\% 8\% 10 8.98259 8.1109 7.36009 6.71008 40 27.35548 19.79277 15.04630 11.92461
Excerpt from the Present Value of an Annuity Due of $1 Table
Periods 2\% 4\% 6\% 8\% 10 9.16224 8.43533 7.80169 7.24689 40 27.90259 20.58448 15.94907 12.87858
a. What is the present value of those investment payments if the first of 40 deposits are made at the end of each quarter?
b. What is the present value of those investment payments if the first of 40 deposits are made at the beginning of each quarter?
Potash Corporation financed the purchase of a building by making semiannual payments of $27,000 for the next twenty years, with the first payment due six months from today. The purchase cost of the building is considered to be the present value of those payments. What was the purchase cost of the building to Potash assuming an annual interest rate of 10%? (Use spreadsheet software or a financial calculator to calculate your answer. Do not round any intermediary calculations, and round your final answer to the nearest dollar.)
A deferred annuity is an annuity for which the first payment is delayed until a future period.
What is the effective interest rate for an investment fund that pays 6% interest compounded semiannually? (Use spreadsheet software or a financial calculator to calculate your answer. Do not round any intermediary calculations, and round your final answer two decimal places, X.XX%.)
An ordinary annuity is a series of equal periodic payments made at the beginning of each period.
The relationship between the future value of a single sum and the corresponding present value of a single sum is determined by two variables. What are those two variables?
Aucutt Incorporated deposits $200,000 every January 1st and July 1st in a savings account for the next five years so that it can purchase a new piece of machinery at the end of five years. The interest rate is 12%. How much money will Aucutt Incorporated have at the end of five years? (Use spreadsheet software or a financial calculator to calculate your answer. Do not round any intermediary calculations, and round your final answer to the nearest dollar.)
The effective interest rate is calculated as the total interest earned during the year divided by the beginning balance of the investment as the first of the year.
When payments take place at the beginning of each period, the series of cash flows is called a(n) ________.
Simple interest is computed on just the accumulated interest left on deposit.
Assume that you have the opportunity to receive $9,000 at the end of each of the next seven years. Given an interest rate of 7%, how much would you be willing to pay for this investment today? (Use spreadsheet software or a financial calculator to calculate your answer. Do not round any intermediary calculations, and round your final answer to the nearest dollar.)
What is the term that describes the value today of a cash flow or series of cash flows to be received or paid in the future?
What is the effective interest rate for an investment fund that pays 4% interest compounded monthly? (Use spreadsheet software or a financial calculator to calculate your answer. Do not round any intermediary calculations, and round your final answer two decimal places, X.XX%.)
Anne wants to accumulate $20,000 by December 31, 2019. To accumulate that sum, she will make twelve equal quarterly deposits of $1,576.98 at the end of March, June, September, and December for the next three years, beginning on March 31, 2016, into a fund that earns interest compounded quarterly. What annual rate of interest must the fund provide to yield the desired sum? (Use spreadsheet software or a financial calculator to calculate your answer. Do not round any intermediary calculations, and round your final answer to the nearest year.)
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