4/7/16

1

SIMPLE

AND

COMPOUND INTEREST

7.0 activate prior knowledge

SimpleInterest

CompoundInterest

SimpleInterestvs.CompoundInterest

•Interestearnedontheprincipalinvestment

•Earninginterestoninterest

Principal istheoriginalamountofmoneyinvestedorsaved

4/7/16

2

Annual interest rate

IMPLE INTERESTFORMULA

Interest paid

Principal(Amount of money invested or borrowed)

Time (in years)

100I = PRT

If you invested $200.00 in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $10.00.

10 = (200)(0.04)T1.25 yrs = T

enter in formula as a decimal I = PRT

100

4/7/16

3

Typically interest is NOT simple interest but is paid semi-annually (twice a year), quarterly (4 times per year), monthly (12 times per year), or even daily (365 times per year).

COMPOUND INTEREST FORMULA

amount at the end

Principal(amount at start)

annual interest rate

(as a decimal)nt

nrPA ⎟⎠

⎞⎜⎝

⎛ += 1time

(in years)

number of times per year that interest in

compounded

4/7/16

4

nt

nrPA ⎟⎠

⎞⎜⎝

⎛ += 1500.08

4

4 (2)

83.585$=A

Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years.

Trypage406#1and2andpage407#1

4/7/16

5

PersonalFinance

7.1Annuities

RegularSavings!

• Annuitiesareoftenusedtosavemoney.• Relativelysmall,regulardepositscanadduptolargesumsofmoneyovertime

4/7/16

6

Annuities

•Anannuity isaseriesofequalpaymentsmadeatregularintervals

•Anordinarysimpleannuity, iswhenpaymentsaremadeattheendofeachcompoundingperiod

• Theamountofannuity isthesumoftheregulardeposits plusinterest

AmountofanAnnuity

• Theamountofanordinarysimple annuitycanbefoundusingatable orformula

4/7/16

7

AmountofAnnuityUsingaTable

a) The amount of the annuity is $2874.48b) The interest earned is $174.48

Example 1 (p.410):Suppose $450 is deposited at the end of each quarter for 1.5 years in an investment account that earns 10% per year compounded quarterlya) What is the amount of the annuity?b) How much interest does the annuity earn?

AmountofAnnuityUsingFormulaExample 2 (p.411):In the annuity in Example 1, $450 is deposited at the end of each quarter for 1.5 years

at 10% per year compounded quarterly.a) What is the amount of the annuity? b) How much interest does the annuity earn?

a) The amount of the annuity is $2874.48

b) The interest earned is $174.48

4/7/16

8

AmountofAnnuityUsingFormulaExample 2 (p.411):In the annuity in Example 1, $450 is deposited at the end of each quarter for 1.5 years

at 10% per year compounded quarterly.a) What is the amount of the annuity? b) How much interest does the annuity earn?

Homework

• P.415#1a,2,3ab,5,6ab,9,10

4/7/16

9

7.2ThePresentValue

PresentValueofanAnnuity

• Thepresentvalueofanannuity istheprincipalthatmustbeinvestedtodaytoprovide theregularpaymentsofanannuity

This formula can only be used when:The payment interval is the same as the compounding periodA payment is made at the end of each compounding periodThe first payment is made at the end of the first compounding period

4/7/16

10

ProvidingforanAnnuityExample 1 - Using Present Value Formula (p.420):Victor wants to withdraw $700 at the end of each month for 8 months, starting 1 month from now. His bank account earns 5.4% per year compounded monthly. How much must Victor deposit in his bank account today to pay for the withdrawals?

CalculatingthePrincipalBorrowedforaLoanExample 2 (p.422):Seema plans to buy a used car. She can afford monthly car loan payments of $300. The car dealer offers Seema a loan at 6.9% per year compounded monthly, for 3 years. The first payment will be made 1 month from the date she buys the car. a)How much can Seema afford to borrow?

4/7/16

11

CalculatingthePrincipalBorrowedforaLoan(cont…)Example 2 (p.422):Seema plans to buy a used car. She can afford monthly car loan payments of $300. The car dealer offers Seema a loan at 6.9% per year compounded monthly, for 3 years. The first payment will be made 1 month from the date she buys the car. b)How much interest will Seema pay on the loan?

TheRegularPaymentofanAnnuity

• Theamountformuladeterminestheaccumulatedvalueoftheregularpaymentsattheend ofanannuity

• Thepresentvalueformula determinesthemoneyneededatthebeginning ofanannuity toprovideregularannuitypayments

• Whenweknowtheamountorthepresentvalue,wecansolvefortheregularpayment.Todo this,werearrangetheappropriateformulatoisolateR.

4/7/16

12

DeterminingPaymentsGiventheAmountExample 3 (p.428):Brianne wants to save $6000 for a trip she plans to take in 5 years. What regular deposit should she make at the end of every 6 months in an account that earns 6% per year compounded semi-annually?

DeterminingPaymentsGiventhePresentValueExample 4 (p.428):Donald borrows $1200 from an electronics store to buy a computer. He will repay the loan in equal monthly payments over 3 years, starting 1 month from now. He is charged interest at 12.5% per year compounded monthly. How much is Donald’s monthly payment?

4/7/16

13

Homework

• P.423#3,4,9,11• P.430#3,6,7