Introduction to Accounting I Professor Marc Smith CHAPTER 1 MODULE 1 Time Value of Money Module 3

The previous time value of money examples had a single payment. This is referred to as a lump sum. Annuity a series of equal payments (either amounts to be received or paid) with each payment having the same time interval between them. A series of equal, annual payments. A series of equal, semi-annual payments. Time Value of Money – Module 3

An annuity with payments occurring at the end of each period is known as an ordinary annuity. End of year 1 $10, Today End of year 2 End of year 3 End of year 4 Time Value of Money – Module 3

An annuity with payments occurring at the beginning of each period is known as an annuity due. Beginning of year 1 $10, Today Beginning of year 2 Beginning of year 3 Beginning of year 4 Time Value of Money – Module 3

In the future value of an ordinary annuity case, we want to know the value of a series of equal cash flows occurring at the end of each period at some point in the future. How much is a dollar received at the end of every year for four years worth in the future (at the end of 4 years)? Future Value of an Ordinary Annuity = Payment x Future Value Annuity Factor i,n Time Value of Money – Module 3

Future Value of Annuity = Payment x Future Value Annuity Factor KEY POINTS 1.The ‘payment’ in the above formula represents the amount of each individual, equal payment. Do not add the payments together. 2.The future value and present value of annuities are NOT reciprocal to each other (like the lump sums) and therefore can not be used interchangeably to solve problems. i,n Time Value of Money – Module 3

Periods 3% 6% 9% 12% Future Value Annuity = Payment x FVA Factor Future Value Annuity = $5,000 x Future Value Annuity = $31,765 If you invest $5,000 at the end of every year for 5 years into a savings account that pays 12% interest compounded annually, you will have $31,765 in your account at the end of the five years. 12% | 5 Time Value of Money – Module 3

Periods 3% 6% 9% 12% Future Value Annuity = Payment x FVA Factor Future Value Annuity = $2,500 x Future Value Annuity = $32,952 If you invest $2,500 at the end of every 6 months for five years into a savings account that pays 12% interest compounded semi-annually, you will have $32,952 in your account at the end of the five years. 6% | 10 Time Value of Money – Module 3

Interest Earned in Part A [annual compounding] $31,765 - ($5,000 x 5) = $6,765 Interest Earned in Part B [semi-annual compounding] $32,952 - ($2,500 x 10) = $7,952 Please note that once again, when the compounding frequency increased (from annual to semi-annual), the future value also increased because you are earning more interest. Time Value of Money – Module 3

In the future value of an annuity due case, we want to know the value of a series of equal cash flows occurring at the beginning of each period at some point in the future. How much is a dollar received at the beginning of every year for four years worth in the future (at the end of 4 years)? To find the future value of an annuity due table factor, multiply the ordinary annuity factor by (1 + i) Time Value of Money – Module 3

Periods 3% 6% 9% 12% Future Value Annuity = Payment x FVAF Future Value Annuity = $2,500 x x 1.06 Future Value Annuity = $34,929 If you invest $2,500 at the beginning of every 6 months for five years into a savings account that pays 12% interest compounded semi-annually, you will have $34,929 in your account at the end of the five years. 6% | 10 Time Value of Money – Module 3 x 1.06