6.7 Day 1 Applying Simple and Compound Interest p303Warm Up Find each % of increase or decrease.

1. from 40 to 59 2. from 85 to 170

* NS1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

(Simple) I = P r t

LO: I will use multiplication strategies to evaluate simple interest.

TIPS:

P + I = A (Amount Total)

• When you deposit money into a bank, the bank pays you interest.

• When you borrow money from a bank, you pay interest to the bank.

I = P r t

Simple interest is money paid only on the principal.

Principal is the amount of money borrowed or invested.

Rate of interest is the percent charged or earned.

Time that the money is borrowed or invested (in years).

Finding Interest and Total Payment on a Loan- To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?

First, find the interest she will pay.

I = P r t Use the formula.

I = ______ ___ __ Substitute. ________ for 9%.

_________ + __________ = _____________

Principal + Interest = Amount Total

Jessica will repay a total of $__________ on her loan.

I = _____

I = P r t Use the formula.

_____= _____ _____ t Substitute values

Determining the Amount of Investment Time- Nancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested?

_____ = ____tThe money was invested for ______years, or ____ years and ____ months.

I = ____ ____ ____

I = ____ The interest is $____. Now find the total.

Computing Total Savings- John’s parents deposited $1000 into a savings account as a college fund when he was born. How much will John have in this account after 18 years at a yearly simple interest rate of 4%?

P + I = A

______ + _______ = A

______ = AJohn will have $__________ in the account after 18 years.

Finding the Rate of Interest- Mr. Twain borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money? P + I = A (Amount Total)

_____ + I = _______ He paid $___ in interest.

Now use the amount of interest paid to find the interest ______ (%).

I = P r t ______= ______ r ___

_______= _______ r Divide both sides by 32,000.

Mr. Twain borrowed the money at an annual rate of _____ or ___%.

6.7 RM & SRe p307

Compound interest is INTEREST PAID on the PRINCIPAL, and ALSO on the INTEREST.

A = final dollar value

P = principal

r = rate of interest

t = time in years

n = number of compounding periods per year.

A = P(1 + ) r n

nt

6.7 Day 2 Compound Interest p303

LO: I will evaluate compound interest using (Simple) I = P r t “and a little more.”

David invested $1800 in a savings account that pays 4.5% interest compounded semi-annually. Find the value of the investment in 12 years.

Substitute.

= 1800(1 + 0.0225)24 Simplify.

= 1800(1 + )0.045 t 2

2(12)

= 1800(1.0225)24 Add inside the parentheses.

A = P(1 + ) r n

nt

Compounding Periods Times per year (n)

Annually 1

Semi-annually 2

Quarterly 4

Monthly 12

After 12 years, the investment will be worth about $__,070.38.

1800(1.70576)= ≈

(Simple) I = P r t “and a little more.”

Kia invested $3700 in a savings account that pays 2.5% interest compounded quarterly. Find the value of the investment in 10 years.

= 3700(1 + 0.00625)__ Simplify.

= 3700(1 + )0.025 t

_(__)

= 3700(1.00625)__ Add inside the parentheses.

A = P(1 + ) r n

nt

After 10 years, the investment will be worth about $_______.

≈ 3700(1.28303)

≈

(Simple) I = P r t “and a little more.”

The Hemmings borrowed $3000 for home improvements. They repaid the loan and $600 in simple interest four years later. What simple annual interest rate did they pay?

Theresa invested $800 in a savings account that pays 4% interest compounded quarterly. Find the value of the investment after 6 years.

A = P(1 + ) r n

nt

RTGO? Quiz Page 308 all

(Simple) I = P r t “and a little more.”

(Simple) I = P r t “and a little more.”