Time Is Money

Objectives• Distinguish between simple and compound interest

• Apply the compound interest formula to determine the future value of a lump-sum investment earning compound interest

• Determine the future value using technology

• Determine the effective interest rate

• Apply the present value formula in a given situation involving compound interest

• Determine the present value using technology

Words To know…• Simple Interest – interest paid on principal amount only

• Compound Interest – interest paid on interest as well as principal amount

• Effective Annual Yield – is also called the APY

• Annual Percentage Yield (APY) – is the true rate of return on an investment

• Present Value – amount that must be invested now at compound interest to reach a given future value

• Future Value – amount that an investment will be worth at a future time if invested at compound interest

Vocabulary • Residual Value– How much a fixed asset is worth at the

end of its lease, or at the end of its useful life

• MSRP– Manufacture Suggested Retail Price

• Lease– legal document for a renter, both the lessee and leaser must uphold the terms of the contract.

• Rebate– “cash back,” offer to consumers for a cash discount on the purchase of a consumer good.

• Finance Charge– fee charged for the use of credit or extension of existing credit.

• Depreciation– decreases in value to wear and tear, decay, decline in price, etc.

Activity

Suppose $10,000 is deposited in a bank at 6.5% annual interest. What is the interest earned after one year?

Suppose you left the money in the account for 10 years. Can the total amount of interest be calculated by multiplying your answer above by 10?

What type of interest would this be?

10,000 0.065 = $650

Maybe: 10 $650 = $6500

Only if it is simple interest.

Compound Interest Formula

If interest is compounded, then the current balance is given by the formula

A = P(1 + r/n)nt

where A is the current balance or compound amount

P is the principal (original amount deposited)

r is the annual interest rate (in decimal form)

n is the number of times per year that the interest is compounded

t is the time in years that money has been invested

Using our Calculator

We have an application on our calculator called Finances. Under this application we have a program called TVM Solver that will solve many of the financial problems that we will deal with in this chapter.

Press the APPS key, select Finances and ENTER

The TVM Solver is the first option under CALC. Hit ENTER and see the list of variables that we need to find values for and which ones we can solve for.

TI TVM Solver

• N = total number of compounding periods• I% = r, where r% is the annual interest rate• PV = present value (amount invested or principal)• PMT = payment• FV = future payment• P/Y = number of payments per year• C/Y = number of compounding periods per year• PMT/END = payment due at the end of the period• PMT/BEGIN = payment due at the beginning of the period

• Use ALPHA Enter on a line to solve for that item

Compound Interest Examples

a. Suppose you deposit $10,000 in an account that has a 6.5% annual interest rate and whose interest is compounded annually. How much do you have after 5 years?

b. If compounded quarterly?

c. If compounded monthly?

N=5, I%=6.5, PV=10000, P/Y=C/Y=1, PMT:ENDFV = $13,700.87

N=5*4, I%=6.5, PV=10000, P/Y=C/Y=4, PMT:ENDFV = $13,804.20

N=5*12, I%=6.5, PV=10000, P/Y=C/Y=12, PMT:ENDFV = $13,828.17