• Write a 200- to 300-word description of the four time value of money concepts: present value, present value of an annuity, future value, and future value of annuity. Describe the characteristics of each concept and provide an example of when each would be used.

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DESCRIPTION OE THE FOUR TIME VALUE OF MONEY CONCEPTS


Present value is the value of a cash flow today.
Usage when a single cash flow is to be discounted to today’s value.
Formula PV = FV / ((1+i) ^n))
Where, PV = Present value
FV = Future Value
i= interest rate per compounding period
n=period
PVIF = Present Value Interest Factor = (1/ ((1+i) ^n))
Example Mr A would receive $1,100 from Mr B after 1 year. Find the present value of the cash flow if Mr A’s interest rate is 10% p.a.
PV = 1100 / (1.1^1) = $1,000
Thus, the present value of cash flow to be received after 1 year is $1,000 today.

Present value of annuity is the value of a series of equal cash flow received in equidistant period, today.
Usage when a series of cash flow is to be discounted to today’s value.
Formula PV = (a/i) (1-(1/ ((1+i) ^n)))
Where, PV = Present value
a = equal cash flow (annuity)
i= interest rate per compounding period
n=no. of annuities
PVIFA = Present Value interest factor of annuity = (1/i) (1-(1/ ((1+i) ^n)))
If cash flow occurs at the beginning of period then the above formula is to be multiplied by (1+i)
Example Mr A would receive $1,000 from Mr B every year for 5 years. Find the present value of the cash flow if Mr A’s interest rate is 10% p.a.
PV = (1000/.1)(1-(1/((1.1^5))) = $3,791
Thus, the present value of cash flow to be received every year for 5 years is $3,791 today.

Future value is the value of a cash flow in future.
Usage when value of a single cash flow is to be computed in future’s date.
Formula FV = PV ((1+i) ^n))
Where, PV = Present value
FV = Future Value
i= interest rate per compounding period
n=period
FVIF = Future Value Interest Factor = ((1+i) ^n))
Example Mr A would receive $1,000 from Mr B today. Find the future value of the cash flow if Mr A’s interest rate is 10% p.a.
FV = 1000 * (1.1^1) = $1,100
Thus, the future value of cash flow after 1 year is $1,100.

Future value of annuity is the value of a series of equal cash flow received in equidistant period, on a future date.
Usage when future value is to be computed for a series of cash flow.
Formula FV = (a/i) (((1+i) ^n)-1)
Where, FV = Future value
a = equal cash flow (annuity)
i= interest rate per compounding period
n=no. of annuities
FVIFA = Present Value interest factor of annuity = (1/i) (((1+i) ^n)-1)))
If cash flow occurs at the beginning of period then the above formula is to be multiplied by (1+i)
Example Mr A would receive $1,000 from Mr B every year for 5 years. Find the future value of the cash flow if Mr A’s interest rate is 10% p.a.
FV = (1000/.1) ((1.1^5)-1)) = $6,105
Thus, the future value of cash flow to be received every year for 5 years is $6,105.

Solve, using the Rule of 72: rate =6%, pv=$7,000, fv= $56,000. Solve for years.

To understand the concept of time value of money, it is important to familiarize yourself with four key concepts: present value, present value of an annuity, future value, and future value of annuity. These concepts help quantify the value of money over time and assist in financial decision-making.

1. Present Value (PV): Present value is the concept that a dollar received in the future is worth less than a dollar received today, due to factors like inflation, opportunity cost, and risk. It represents the current value of a future cash flow, considering a chosen interest rate or discount rate. Present value is commonly used in determining the worth of investments, loans, and real estate. For example, when deciding whether to invest in a particular project, you would calculate the present value of expected future cash flows to determine its profitability.

2. Present Value of an Annuity (PVA): An annuity refers to a series of regular, fixed payments received or paid over a specified period. The present value of an annuity measures the current worth of these future cash flows, considering an interest or discount rate. PVA is often used in calculating mortgage repayments, lease agreements, or retirement savings. For instance, when deciding on a mortgage, you would determine the present value of the monthly payments to assess affordability.

3. Future Value (FV): Future value represents the expected value of an investment or cash flows at a specific time in the future. It takes into account compounding interest and the time value of money. FV is crucial in estimating the growth of savings, investments, or retirement funds. For example, when saving for retirement, you would calculate the future value of regular contributions to determine the accumulated amount at retirement age.

4. Future Value of an Annuity (FVA): The future value of an annuity measures the expected future worth of a series of regular cash flows, considering a specific interest rate. FVA is commonly used in planning for retirement, estimating education expenses, or calculating loan repayments. For instance, when assessing how much you need to save each month for your child's college education, you would calculate the future value of regular contributions to cover the expenses.

In summary, present value and future value concepts help assess the worth of single cash flows, while the annuity versions consider a series of regular cash flows. By applying these time value of money concepts, individuals and businesses can make informed financial decisions.