Lesson 2- Time Value Money Flashcards
What is the time value of money? How is it related to opportunity costs?
The time value of money is a powerful principle that can be used to explain how money grows over time. When you spend money, you incur an opportunity cost of what you could have done with that money had you not spent it. For example, if you spent $2,000 on a vacation rather than saving it, you would have incurred an opportunity cost of the alternative ways that you could have used the money. You can use the time value of money to compute the actual cost of the opportunity.
Define interest. Define and describe simple interest and compound interest.
Interest is the rent charged for the use of money. Depending on whether you have borrowed or loaned money, you will either pay or receive interest, respectively. Simple interest is interest on a loan computed as a percentage of the loan amount, or principal. The interest earned or paid is not reinvested. Simple interest is measured by multiplying the principal, the interest rate applied to the principal, and the loan’s time to maturity (in years). Compound interest refers to the process of earning interest on interest.
List three methods that can be used to solve time value of money problems.
For simple problems a time value of money table may be used to calculate the future or present value of a single dollar amount. Other methods that may be used to solve time value of money problems include time value of money formulas and financial calculators.
To what types of cash flows is the time value of money concept most commonly applied?
The time value of money is most commonly applied to two types of cash flows: a single dollar amount (also referred to as a lump sum) and an annuity. An annuity refers to the payment of a series of equal cash flow payments at equal intervals of time.
What inputs are required when calculating the future value of a single dollar amount using a formula?
The inputs required when calculating the future value, FV, of a single dollar amount using a formula are the present value of an investment (PV), the annual interest rate, i, (expressed as a decimal), the number of compounding periods per year (n), and time, t, (in years).
How many compounding periods per year are there when interest is compounded annually? Semi-annually? Quarterly? Monthly? Weekly? Daily?
When interest is compounded annually, semi-annually, quarterly, monthly, weekly, or daily, there are 1, 2, 4, 12, 52, or 365 compounding periods, respectively.
What is the future value interest factor? What is the formula for determining the future value of a single dollar amount when using the future value interest factor table? What information must be known in order to find the correct future value interest factor?
The future value interest factor (FVIF), is a factor multiplied by today’s savings to determine how the savings will accumulate over time. The factor is determined based on an annual interest rate where the number of compounding periods is one. The formula for determining the future value of a single dollar amount when using the future value interest factor is:
FV = PV × FVIFi,n
In order to find the correct future value interest factor, you must know the interest rate and the number of years the money is invested.
What should you do each time before you use a financial calculator to solve a time value of money problem?
Clear the existing TVM values in the calculator’s TVM worksheet by entering 2ND CLR TVM.
What is the difference between a cash inflow and a cash outflow?
A cash inflow (for example, income received from an investment) should be entered as a positive number. A cash outflow (for example, an amount invested) should be entered as a negative number. The +/- key on the TI BA II Plus is used to convert a positive number to a negative number, and vice versa.
On the Texas Instruments BA II Plus calculator, what calculator keys do you have to press in order to access the number of compounding periods per year function?
In order to access the number of compounding periods per year function on your calculator, press 2ND P/Y, then press the down arrow.
What is discounting?
Discounting is the process of obtaining present values.
Describe some instances when determining the present value of an amount is useful.
Suppose you need $20,000 to purchase a car in 3 years. You may want to determine how much money you need to invest today to have the $20,000 in three years. Another instance where determining the present value is useful would be if you want to pay off a loan today that will, for example, be paid over 3 years. In this case, you want to know the present value of these future payments.
What formula is used when determining the present value of a single dollar amount?
The formula for the present value of a single dollar amount is:
PV= FV/(1+i/n)nt
What is the present value interest factor? What is the formula for determining the present value of a single dollar amount when using the present value interest factor table?
The present value interest factor is a factor multiplied by the future value to determine the present value of that amount. The formula for determining the present value of a single dollar amount when using the present value interest factor is:
PV = FV × PVIFi,n
Define annuity. Define and describe the two main types of annuities.
An annuity refers to the payment of a series of equal cash flow payments at equal intervals of time and subject to the same interest rate. An ordinary annuity is a stream of equal payments that are received or paid at equal intervals in time at the end of a period. An annuity due is a series of equal cash flow payments that occur at the beginning of each period. Thus, an annuity due differs from an ordinary annuity in that the payments occur at the beginning instead of the end of the period. The most important thing to note about an annuity is that if the payment or interest rate changes over time, the payment stream does not reflect a single annuity.
What formula is used to determine the future value of an annuity?
The formula used to determine the future value of an annuity is:
FV = PMTx[((1+i)n-1)/i]
What is the future value interest factor for an annuity? What is the formula for determining the future value of an annuity when using the future value interest factor for an annuity table?
The future value interest factor for an annuity, FVIFA, is a factor multiplied by the periodic savings level (annuity) to determine how the savings will accumulate over time. The formula for the future value interest factor for an annuity, when using a table, is:
FVA = PMT × FVIFAi,n
When using a formula or annuity table, what must you do to adjust your calculation for an annuity due?
An annuity formula or table will provide the future value for an ordinary annuity. In order to adjust your calculation for an annuity due, you would multiply the annuity payment generated by multiplying the value from the table by (1 + i).
What formula is used to determine the present value of an annuity?
The formula used to determine the present value of an annuity is:
PV = PMT x [(1-[1/(1+i)n])/i]
What is the present value interest factor for an annuity? What is the formula for determining the present value of an annuity when using the present value interest factor for an annuity table?
The present value interest factor for an annuity, PVIFA, is a factor multiplied by a periodic savings level (annuity) to determine the present value of the annuity. The formula for the present value interest factor for an annuity, when using a table, is:
PVA = PMT × PVIFAi,n
What would be the number of compounding periods (n) when determining the future value of an annuity, where money is invested monthly over a five-year period?
60 (5yrs x 12 mos./yr)
Define the terms nominal interest rate and effective interest rate. Why is it important to be able to distinguish between these two different rates?
The nominal interest rate is the stated, or quoted, rate of interest. It is also known as the annual percentage rate (APR). The effective interest rate is the actual rate of interest that you earn, or pay, over a period of time. It is also known as the effective yield (EFF). When comparing two or more interest rates, the nominal interest rate is not useful because it does not take into account the effect of compounding. In order to make objective investment decisions regarding loan costs or investment returns over different compounding frequencies, the effective interest rate has to be determined. The effective interest rate allows for the comparison of two or more interest rates because it reflects the effect of compound interest.
In questions 23 through 26, indicate whether you would solve for the future value of a single sum, the present value of a single sum, the future value of an annuity, or the present value of an annuity.
you want to know how much you must deposit today to have $5,000 in five years.
The present value of a single sum.
You plan to contribute $300 per month to your company’s retirement plan and want to know how much you will have at retirement.
The future value of a single sum.
You received $500 as a gift for graduation and want to know how much it will be worth in three years if you deposit it in a savings account.
The future value of a single sum.
You must decide between accepting a lump sum settlement and annual payments.
The present value of an annuity.
