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The time value of money
- that money can be invested today to earn interest and grow to a larger dollar amount in the future.
- *has nothing to do with the worth or buying power of the $.
- Useful in valuing several assets and liabilities
- * involves PV, leases, bonds, pension obligations, and certain notes rec and payables.
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Interest
Is the amount of money paid or received in excess of the amount borrowed or lent.
- The rent paid for the use of money for some period of time.
- The interest gives money its time value
- *Typically stated as annual rates or APRs
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Simple interest
computed by multiplying an initial investment times both the applicable interest rate and the period of time for which the money is used.
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Compound Interest
- includes interest not only on the initial investment but also on the accumulated interest in previous periods.
- Daily compounding is common in savings accts.
- More rapid compounding has the effect of increasing the actual rate which is called the effective rate. at which the money grows per year.
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Effective rate
- Often reffered to as the annual yield.
- is the rate at which money actually will grow during a full year.
- When interest is compounded more freq than once a year the equation:
- Yield = (1+i/p)p - 1
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Future value of a single amount
- FV = I(1+i)nFV = FV of the invested amount
- I = Amount invested at the beginning of the period
- i = Interest rate
- n - Number of compunding periods
- Can be figured by using table 1
- The FV of a singla amount is the amount of money that a dollar will grow to at some point in the future.
- *requires inclusion of compound interest
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Present Value of a single amount
- The PV value of a single amount is today's equivalent to a particular amount in the future.
- PV = FV/(1+i)n
- *requires removal of compound interest
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How much is a dollar worth today?
is worth more than a dollar to be received in the future
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What is the difference between present value of cash flows and their future value?
represents the time value of money.
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What is interest?
is the rent paid for the use of money over time
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What is the future value of a single amount?
- is the amount of money that a dollar will grow to at some point in the future.
- It is computed by multiplying the single amount by (1+i)n . The Present value of $1 table simplifies the calculation of the present value of any future amount.
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What are the 4 variables in the process of adjusting single cash flow amounts for the time value of money?
PV. FV, i and n. If you know any of the three, the fourth can be computed
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What is an annuity?
is a series of equal sized cash flows occuring over equal intervals of time. An ordinary annuity exists when the cash flows occur at the end of each period.
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What is the future value of an ordinary annuity?
FVA is the future value of a series of equalsized cash flows with the payment taking place at the end of the first compounding period. The last payment will not earn any interest since it is made at the end of the annuity period.
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What is the future value of an annuity due?
FVAD is the future value of a series of equal sized cash flows with the first payment taking place at the beginning of the annuity period (the beginning of the first compounding period)
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What is the present value of an ordinary annuity?
PVA is the present value of a series of equal sized cash flows with the first payment taking place at the end of the first compounding period.
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What is the present value of an annuity due?
PVAD is the present value of a series of equal sized cash flows the first payment taking place at the beginning of the annuity period.
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What is the present value of a deferred annuity?
is the present value of a series of equal sized cash flows with the first payment taking place more than one time period after the date of the agreement.
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What are the 4 variables in present value problems involving annuities?
PVA or PVAD, the annuity amount, the number of compounding periods (n) and the interest rate (i). If you know any of the three, you can determine the fourth.
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What do most applications of the time value of money involve?
the present values of annuities
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How is the initial valuation of long term bonds determined?
by calculating the present value of the periodic stated interest payments and the present value of the lump sum payments made at maturity.
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What do certain leases require a lessee to compute?
the present value of future lease payments to value the leased asset and corresponding lease obligations.
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What do pension plans require?
the payment of deffered annuities to retire.
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The rate at which money actually will grow during a full year is called the
Time value of money rate.
Compound rate.
Simple rate.
Effective rate.
Effective rate.
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If you invest $140 in a savings account for one year at your local bank yielding 12% when the inflation rate is 14% which of the following is true?
A. The future value of the investment is $157.
B. Assuming that the interest compounds annually, you would have more than $157 at the end of the first year.
C. Your money would be worth more than the $140 you had a year earlier.
D. All of the choices are correct.
A. The future value of the investment is $157.
140 x .12 = 157 (this multiple choice question has been scrambled)
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Jane invests $1,900 in a saving account at Third Bank for 3 years. The investment pays 20%, compounded annually. At the end of the third year, how much would Jane have in her savings account assuming she did not withdraw any money during the 3 years? (Round your answer to the nearest dollar amount.)
$3,040
$3,283
$3,290
$2,290
$3,283
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Which of the following statements concerning future values is true?
a. To determine the future value of any invested amount, divide the invested amount by the Future Value of $1 table value at the intersection of the column for the desire rate and the row for the corresponding number of periods from a future value table.
b. The "n" in the future value formula refers to the number of years.
c. If you're computing the future value two years from today of $1,000 invested at 12% with quarterly compounding, the number of periods is eight and the compounding rate is 3%.
d. All of the choices are true regarding future value.
If you're computing the future value two years from today of $1,000 invested at 12% with quarterly compounding, the number of periods is eight and the compounding rate is 3%.
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Which of the following statements is false concerning future value?
a. At 2% annual interest, the future value of a sum of money will always be greater than its present value.
b. The future value of a single amount is the amount of money that a dollar will grow to at some point in the future.
c. To determine the future value of any invested amount, multiply it by the Future Value of $1 table value at the intersection of the column for the desired rate and the row for the number of compounding periods.
d. In the future value formula, "n" refers to the number of years.
In the future value formula, "n" refers to the number of years
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Interest
Amount of money paid/received in excess of amount borrowed/lent.
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Monetary asset
Claim to receive a fixed amount of money.
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Compound interest
Interest calculated on invested amount accumulated interest.
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Simple interest
Computed by multiplying an invested amount by the interestrate.
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Present value of a single amount
amount of money required today that is equivalent to a given future amount
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Annuity
A series of equal sized cash flows
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Annuity Due
First cash flow occurs on the first day of the agreement
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future value of a single amount
the amount of money that a doller will grow to
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ordinary annuity
first cash flow occurs one period after agreement begins
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effective rate or yield
the rate at which money will actually grow during a year
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nonmonetary asset
no fixed dollar amount attached
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time value of money
money can be invested today and grow to a larger amount
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monetary liability
obligations to pay a sum of cash, the amount of which is fixed
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