SIMPLE AND COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you!

Why do you need to know how to calculate interest? (where might you use interest?)

Interest Rates as of Apr Loan Rates –Credit Cards 15-30% –College 6-8% –Home loans 3-4% –Car loans 2-5% Savings Rates –Savings rates ~0.05% –Money markets rates 0.1 – 0.5% maybe –CDs 1-2%

Vocabulary terms Principal – the amount of money your borrow Interest - a fee that you pay the lender in exchange for borrowing the money Interest rate - is the rate at which interest is paid by for the use of money that you borrow (percentage)

What is “SIMPLE INTEREST”? A quick method of calculating the interest charge on a loan. Simple interest is determined by multiplying the interest rate by the principal by the number of periods. Simple Interest = P * I * N Where: P is the loan amount I is the interest rate N is the duration of the loan, using number of periods (for example 6 years)

Example: You borrow $10,000 for 3 years at 5% simple annual interest. Simple interest = p * i * n $10,000 *.05 * 3 = $1,500 The interest you will pay after 3 years is $1, 500

What Is “Compound Interest”? Compound interest is the interest you earn on interest! M = P( 1 + i ) n M is the final amount including the principal. P is the principal amount. i is the rate of interest per year. n is the number of years invested.

For example, you borrow $10,000 for three years at 5% annual interest compounded annually : Interest year 1 p * i * n = 10,000 *.05 * 1 = 500 Interest year 2 = (p 2 = p 1 + i 1 ) * i * n = (10, ) *.05 * 1 = 525 Interest year 3 = (p 3 = p 2 + i 2 ) * i * n = (10, ) *.05 * 1 = Total interest earned over the three years = = $1, Compare this to 1,500 earned over the same number of years using simple interest.

Compound Interest Illustration Using Basic Math If you have $ and it earns 5% interest each year, you'll have $ at the end of the first year. But at the end of the second year, you'll have $ Not only did you earn $5.00 on the $ you initially deposited—your original "principal"—but you also earned an extra $0.25 on the $5.00 in interest. Twenty-five cents may not sound like much at first, but it adds up over time. Even if you never add another dime to that account, in 10 years you'll have over $ through the power of compound interest, and in 25 years you'll have almost $

When investing/saving money: Compound interest is your best friend! How much does a slice of pizza cost? Would you believe nearly $65,000? If a slice of plain pizza costs $2.00, and you buy a slice every week until you're old enough to retire, you'll spend $5,200 on pizza. If you give up that slice of pizza and invest the money instead, earning 8% interest compounded every year for 50 years, you'll have over $64,

Rule of 72 Years to double = 72 / Interest Rate Really just a “rule of thumb” — is a great way to estimate how your investment will grow over time. If you know your investment’s expected rate of return, the Rule of 72 can tell you approximately how long it will take for your investment to double in value. Simply divide the number 72 by your investment’s expected rate of return (ignoring the percent sign). Assuming an expected rate of return of 9 percent, your investment will double in value about every 8 years (72 divided by 9 equals 8).

Rule of 72 – useful for estimates At 6% interest, your money takes 72/6 or 12 years to double. To double your money in 10 years, get an interest rate of 72/10 or 7.2%. If college tuition increases at 5% per year (which is faster than inflation), tuition costs will double in 72/5 or about 14.4 years. If you pay 15% interest on your credit cards, the amount you owe will double in only 72/15 or 4.8 years!

More on Compound Interest Knowing how quickly your investment will double in value can help you determine a “ballpark” estimate of your investment’s future value over a long period of time. Let’s say that you invest $10,000 in a retirement plan. What will your investment be worth after 40 years, if you don’t make any additional contributions? Assuming an expected rate of return of 9 percent, the total approximate value of your investment would double to $20,000 in 8 years, $40,000 in 16 years, and $80,000 in 24 years, $160,000 in 32 years, and $320,000 in 40 years.

Compounding Interest – your enemy when borrowing money! Borrowing money for college. –$100,000 for 5 years (6.80%) Monthly Loan Payment: $1, Number of Payments: 60 Cumulative Payments: $118, Total Interest Paid: $18,241.82

So DON’T take loans unless you absolutely have to! $10,000 in debt; 17% interest rate on credit card – if unpaid totally for 1 year = $1700 in interest payments Left for 6 years – becomes $21,924 in interest payments –And the principal is still due!

Scenario: Buying my first new car Car cost: $25,000 (minus the cost of my old car traded in = $19,000) Bank account: $20,000 Monthly expenses: $4,000 Monthly salary: $5,000 Should I get a loan? Or pay cash?

Should I get a loan? NO Always keep an emergency fund of 3-6 months expenses. –Buying a car for $19,000 would leave only $1,000 in my account, when my costs are ~$4,000 a month.

Annual interest rate IMPLE INTEREST FORMULA Interest paid Principal (Amount of money invested or borrowed) Time (in years) 100 I = PRT

If you invested $ in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $ = (200)(0.04)T 1.25 yrs = T 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). enter in formula as a decimal I = PRT 100

COMPOUND INTEREST FORMULA amount at the end Principal (amount at start) annual interest rate (as a decimal) time (in years) number of times per year that interest in compounded

(2) Effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as that made compounding. This is found by finding the interest made when compounded and subbing that in the simple interest formula and solving for rate. Find the effective rate of interest for the problem above. The interest made was $ Use the simple interest formula and solve for r to get the effective rate of interest. I = Prt 85.83=(500)r(2) r = = 8.583% Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years.