Mr. Sardinha Math 10

7.1 Simple and Compound Interest

Simple Interest

Simple interest is based on three pieces of information: the principal, the rate, and the time.

Interest: The fee charged for the use of money.

Principal: The money on which interest is paid.

Rate: The percent charged for money borrowed. This is given as a yearly (annual) rate.

Example 1: Find the future amount of an $8000 simple interest investment for 5 years at 6%.

Example 2: A $2100 payment is due in 15 months. Find the principal if the money is borrowed at 11%

simple interest.

Simple Interest and Future Amount

Interest = Principal x Rate x Time

I = P ∙ r ∙ t

Future Amount = Principal + Interest

A = P + I or A = P(1 + r ∙ t)

Example 3: Yazia borrowed $5200 at 7.5% simple interest to build a swimming pool.

If she paid $2340 interest, find the term of the loan and the monthly payments.

Discount Loans

Sometimes the interest on a loan is paid up front by deducting the amount of the interest the lender

gives you. This type of loan is called a discounted loan.

Example 4: Noushin obtained a 2 year $6000 loan for university. The rate was 8% simple interest and

the loan was a discounted loan.

a) Find the discount.

b) Find the amount of money Noushin received.

c) Find the actual interest rate.

Compound Interest

When interest is calculated on the principal plus any previously earned interest it is called compound

interest.

To derive a formula for compound interest you need to use the distributive rule, a + ab = a(1 + b),

many times to see a pattern. Remember, the interest for any year is based on principal plus interest of

the year before.

Interest can be compounded more than once a year, such as semi-annually, quarterly, monthly, or daily.

To calculate the interest rate for one compounding period, divide r by the number of compounding

periods per year, n. The number of times interest is compounded in t years is n ∙ t.

For compound interest questions, below are typical scenarios for n:

interest calculated monthly: n = interested calculated bi-monthly n =

interest calculated quarterly: n = interest calculated daily: n =

interest calculated annually: n = interest calculated semi-anually: n =

interest calculated weekly: n = interest calculated bi-weekly: n =

Compound Interest Formula

𝐴 = 𝑃 (1 +𝑟

𝑛)𝑛𝑡

where: A = the final amount, P = principal, or initial amount, r = rate of yearly interest,

n = number of times yearly interest is compounded per year, t = time in years

Example 5: Suppose that $8000 is invested for 3 years at 6%.

a) Find the amount of simple interest paid.

b) Find the compound interest, if interest in calculated annually.

Example 6: To have savings for university, the parents of a child invest $25 000 in a savings plan

paying 6% interest compounded quarterly. How much money will they have in 18 years?

Example 7: How much would you have to invest into a 10 year bond paying 4.2% compounded

weekly to make it worth $5000 at the end of its term?

Mickelson Workbook: pp.281–283 #1 – 4 (all), 5 – 12 (any six questions)