Chapter 5 Time Value of Money Concepts Intermediate Accounting 1

Keys on a financial calculator defined:

N= number of periods %I= interest rate PV = present value FV = future value PMT = annuity payments CPT = compute button

You pay $3,500 at the end of each quarter for 3 years at a discount rate of 12% (annual rate) for your car payments. What is the value of your car today?

PV = $34,839.01

Interest

The amount of money paid or received in excess of the amount borrowed or lent.

Future value (FV) of $1

The amount of money that a dollar will grow to at some point in the future.

Present value (PV) of $1

The amount of money today that is equivalent to a given amount to be received or paid in the future.

Future value of an annuity due (FVAD) of $1

The future value of a series of equal sized cash flows with the first payment taking place at the beginning of the annuity period.

Future value of an ordinary annuity (FVA) of $1

The future value of a series of equal-sized cash flows with the first payment taking place at the end of the first compounding period.

Future value

The future value of a single amount is the amount of money that a dollar will grow to at some point in the future.

Present value of an annuity due (PVAD) of $1

The present value of a series of equal-sized cash flows with the first payment taking place at the beginning of the annuity period.

Present value of an ordinary annuity (PVA) of $1

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.

Interest rates are typically stated as

annual rates.

In an annuity due, cash flows occur at the

beginning of each period.

Monthly =

divide by 12

Semiannually =

divide by 2

Quarterly =

divide by 4

In an ordinary annuity, cash flows occur at the

end of each period.

The time value of money means that

money can be invested today to earn interest and grow to a larger dollar amount in the future.

FV= 80,000 PV = 44,421 i = 4% Solve for n

n = 15

Calculate the present value of a $240,000 payment received 2 years from now at an annual discount rate of 8%

n=2 i=8% PVF= 0.85734 240,000 x 0.85734 = $205,761.60 (calculator may give you 205,761.32)

Calculate the future value at the end of 3 years for $12,500 compounded semiannually at a 10% (annual) rate.

n=6 i=5% FVF= 1.34010 12,500 x 1.34010 = $16,751.25 (calculator may give you $16,7510.20)

Compound interest Includes interest not only on the initial investment but also on

the accumulated interest in previous periods.

In situations when the compounding period is less than a year,

the interest rate per compounding period is determined by dividing the annual rate by the number of periods.

The higher the time value of money,

the lower is the present value of a future amount.

The present value of a single amount is

today's equivalent to a particular amount in the future.