INTEREST

Chapter 9 sec 2

QUESTIONS How many of you have a savings account?

How many of you have loans?

What do these 2 questions have in common?

SOLUTION Answer:Interest.

TYPES OF INTEREST

1) Simple interest.

2) Compound interest.

SIMPLE INTERESTDef. I = Prt

I is the interest earnedP is the principle (deposit)

r is the interest ratet is the time (yrs)

PROBLEMS If you deposit $300 in a bank savings account paying 3.5% annual interest, how much interest will the deposit earn in 4 years if the bank computes the interest using simple interest?

HOW TO SOLVE First change the % to decimals.

Second use the simple interest equation.

I = Prt = 300*.035*4 = 42 In 4 years you will earn $42

FIND THE FUTURE VALUE To find the future value of an

account that pays simple interest, the formula

A is the future value P is the principle r is the annual interest rate t is the time (yrs)

rtPA 1

COMPUTING THE FUTURE VALUE

Assume that you deposit $1500 in the bank account paying 2.8% annual interest and leave the money there for 5 years. Use the simple interest formula to compute the future value of this account.

SOLUTION P = 1500 r = 2.8% = .028 t = 5

A = 1500(1+.028*5) = 1710 At the end of 5 years you will have $1,710 in your account.

FIND THE PRESENT VALUE

Assume that you plan to save about $3000 to take a trip to Europe in 2 years. Your bank offers you a CD (Certificate of Deposit) that pays 3.4% annual interest computing using the simple interest. How much must you put in this CD now to have the necessary money in 2 years.

Remember that you are using this equation.

A = 3000 r = 3.4% = .034 t = 2

rtPA 1

SOLUTION 3000 = P (1 + .034*2) 3000 = P (1.068)

99.2808068.13000

P

You will have to put at least $2809.00 to guarantee that if you put this amount in the CD now, in 2 years you will have the $3000 you need for your trip to Europe.

COMPOUND INTEREST If the money in a bank account

has earned interest, the bank should compute the interest due, add it to the principle, and then pay interest on this new, larger amount. This is in fact the way most bank accounts work. Interest that is paid on principal plus previously earned interest is the compound interest.

COMPOUND INTEREST FORMULA

A is the future amount P is the principle r / m is the annual rate divided by the

number of compounding periods per year

n is which the number of compounding periods

n

mrPA

1

HOW DOES “NO PAYMENTS UNTIL…” WORKS

On the certain commercials there is a couch on sale for $3700 and what really makes the deal attractive is that there is no money down and no payments due for 6 months.

This means that you do not need to make payments, and the dealer or store is not loaning you the money for 6 months for nothing.

You decide to get the couch and borrow $3700 and, in 6 months, your payments will be based upon that fact. Assuming that your dealer is charging an annual interest rate of 18%, compounded monthly, what interest will accumulate on your purchase over the next 6 months.

SOLUTION

We know certain variables. A = unknown P = 3700 r = 18% = 0.18 m = 12 (monthly) n = 6 (months)

= 3700(1.015)^6 = 3700*1.09344 = 4045.74

6

1218.013700

A

The accumulated interest is $4045.74 – $3700 =

$345.74

FINDING THE PRESENT VALUE Your family just had a child

(Congratulations), as a parent you want your child to go to college. You want to deposit money into a tax free account, and assuming that the account has an annual interest rate of 5.2% and that the compounding is done quarterly. How much must the parent deposit now so that the child will have $75,000 at the age of 18?

SOLUTION Using the compound interest

formula

We know certain values. A = 75,000, r = 5.2% = 0.052,

m = 4, n = 72 (18*4 = 72)

n

mrPA

1

Solve the fraction first. Do the exponent next. Divide the number to get P

72

4052.01000,75

P

PP 534.2013.1 72

47.29592534.2000,75

P

A deposit of $29593.00 (round up) now will guarantee $75,000 for college in 18 years.