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Appendix B: Time Value of Money
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B., C., and D.
Summarize what the old saying "Time is Money" means by choosing all of the statements below that reflect its mean. (Check all that apply.)
A. It reflects the notion that management can increase profitability if it has more timely information about the demographics of an area.
B. As we carry the balance of debt, we accumulate interest costs on it.
C. The value of our assets change because of interest earned on the assets.
D. It reflects the notion that as time passes, the value of our assets and liabilities change.
Interest
__________ is payment by the borrower to the owner of an asset for its use.
Present Value
The __________ (present value/future value) concept is important when we want to know how much we must invest now in order to have a certain sum of money some time in the future.
A., B., and D.
Explain what future and present value computations enables us to do by selecting all of the correct statements below. (Check all that apply.)
A. They enable us to measure or estimate the interest component of holding assets or debt over time.
B. The future value computation is important when we want to know the value of present-day assets at a future date.
C. Present and future value computations allow us to better budget our finances so that liquidity is reduced.
D. The present value computation is important when we want to know the value of future-day assets today.
B. and C.
Review the statements below and determine which are correct regarding compounding in regards to interest.
A. In order to determine the future value or present value of a sum of money, the number of compounding periods is irrelevant.
B. Interest can be compounded daily, monthly, quarterly, or annually.
C. In the present value formula, annual interest can be transformed into interest earned per (n) periods.
D. Compounded quarterly interest is another name for simple annual interest.
Present Value of a Single Amount
The formula to compute the __________ is:
p = f/(1+i)^n
Where p = present value; f = future value; i = interest per period; and n = number of periods.
$396.90
Assume that we want to have $500 three periods from today. Use the present value of a single sum formula to calculate how much we must invest now, at an interest rate of 8% in order to have the $500 in the future: p = f/(1+i)^n
Present Value of 1 Formula
The formula to compute the __________ is:
p = 1/(1+i)^n
Where p = present value; i = interest per period; and n = number of periods.
$708.40
Jack is considering an investment that is expected to return $1,000 four years from now. Of he wants a 9% return, calculate the amount of money he is willing to pay for this investment by using the Present Value of 1 table shown.
B., C., and E.
Identify the required components needed to determine the present value of a sum. (Check all that apply)
A. The number of days in a partial year
B. The number of periods the sum will be earning interest
C. The future amount of money needed
D. The risk factor of not receiving payment
E. The interest rate charged
Times and Year
The present value or future value of a sum of money can be calculated as long as we know the number of __________ (days, times, years) that interest will be compounded within one __________ (year, month, day).
Future Value of a Single Amount
The formula to compute the __________ is:
f = p x (1+i)^n
Where p = present value; f = future value; i = interest per period; and n = number of periods.
Future Value of 1
The formula to compute the __________ is:
f = (1+i)^n
Where f = future value; i = interest per period; and n = number of periods.
B. 4 years
Maurice invests $4,500 today earning 6%. He wants to know how many years it will take to accumulate to $5681.25. Calculate how many years he will need to invest the money by using the Future Value of 1 table shown.
A. 3 years
B. 4 years
C. 2 years
D. 5 years
Annuity
An __________ is a series of equal payments occurring at equal intervals.
Ordinary Annuity
An __________ is defined as equal end-of-period payments at equal intervals.
Today, Multiple, and Future
A person can use the present value concept and apply it to an annuity to calculate how much money he has to invest __________ (today, tomorrow) in order to receive __________ (multiple, one) periodic payment(s) in the __________ (present, future).
Present Value of an Ordinary Annuity
The formula to compute the __________ is:
p = PMT x [1 - (1/(1+i)^n)]/i
Where p = present value; PMT = payment per period; i = interest per period; and n = number of periods.
Future Value of an Ordinary Annuity
The formula to compute the __________ is:
f = PMT x [((1+i)^n) - 1]/i
Where f = future value; PMT = payment per period; i = interest per period; and n = number of periods.
Present Value of an Annuity of 1
The formula to compute the __________ is:
p = [1 - 1/(1+i)^n]/i
Where p = present value; i = interest per period; and n = number of periods.
Future Value of an Annuity of 1
The formula to compute the __________ is:
f = [((1+i)^n) - 1]/i
Where f = future value; i = interest per period; and n = number of periods.
$9,245.80
Jack is considering a project that will return $2,000 at the end of each year for 6 years. He wants a return of 8%. Use the Present Value of an Annuity of 1 table below to determined how much he is willing to pay for the project right now.
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