Wize High School Grade 11 Math Textbook > Financial Applications

Simple Interest
Borrowing/Loaning Money
When someone borrows money, they will eventually have to pay back the original amount of money they borrowed (principal) plus an additional amount of money (interest).

Must pay back: Principal + Interest\text{Must pay back}: ~\boxed{\text{Principal}~+~\text{Interest}}Must pay back: Principal + Interest​

Investing Money
When someone invests their money, they are hoping to "grow" their money so that eventually, they will get back the original amount of money that they invested (principal) plus an additional amount of money (interest).

Will get back: Principal + Interest\text{Will get back}: ~\boxed{\text{Principal}~+~\text{Interest}}Will get back: Principal + Interest​

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Simple Interest
To calculate how much "interest" needs to be added on top of the principal, some people use the idea of simple interest -- the interest will be a fraction/percentage of the original principal, this is indicated by the interest rate.

Notice that the total amount of money (principal + interest) grows linearly.

Wize Tip
Interest rates are usually given as a percentage "per year", this can also be called "per annum".
For example: 3% or 3%/a both mean that each year, the interest will be 3% of the original principal.
In calculations, use the decimal form of the percentage by dividing it by 100
E.g. 3%=3100=0.033\% = \dfrac{3}{100} = 0.033%=1003​=0.03


Example

James borrows $1000 from the bank at 5%/a simple interest.
How much interest is owed every year? $1000(0.05) = $50
After 10 years, how much total interest must be repaid? 10($50) = $500
After 10 years, what is the total amount owed? $1000 + $500 = $1500
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Simple Interest Formulas
Total Interest

The total interest of an investment or loan with principal PPP for ttt years at r%/ar\%/ar%/a simple interest is:

I=Prt\boxed{\quad
I = Prt
\quad}I=Prt​

Total Amount

The total amount earned on an investment (or owed on a loan) is the sum of the principal and the total interest:

A=P+IA = P + IA=P+I

Substituting the formula for the total interest, III, and the common factoring, we get:

A=P(1+rt)\boxed{\quad
A = P(1 + rt)
\quad}A=P(1+rt)​

Wize Tip
Both the total interest, I(t)I(t)I(t), and the total amount, A(t)A(t)A(t), are linear functions of time.

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Example: Simple Interest
Amanda gets a line of credit (loan) from the bank for $12,000 at 9%/a simple interest. 
When she returns to pay it back in 18 months, how much must she repay the bank? 

Start by listing the given values:
The principal is P=12000P = 12000P=12000
The interest rate is r=9%=0.09r=9\%=0.09r=9%=0.09
The time must be in years, so we must divide the number of months by 12: t=18 months12 monthsyear=1.5 yearst=\dfrac{18\ {\rm months}}{12\ \frac{\rm months}{year}}=1.5\ {\rm years}t=12 yearmonths​18 months​=1.5 years
Now we can simply apply the formula for the total amount:

A=P(1+rt)=12000(1+0.09(1.5))=12000(1+0.135)=12000(1.135)=$ 13620\begin{aligned}
A &= P(1+rt)\\
&= 12000(1+0.09(1.5))\\
&= 12000(1+0.135)\\
&= 12000(1.135)\\
&= \boxed{\$\ 13620}
\end{aligned}A​=P(1+rt)=12000(1+0.09(1.5))=12000(1+0.135)=12000(1.135)=$ 13620​​
Therefore, Amanda must pay $13620 to pay off her loan after 18 months.

How much goes towards paying interest?

We could use the formula I=PrtI=PrtI=Prt, or we can use our previous result.

Since the total amount is the principal plus the interest, A=P+IA=P+IA=P+I, we can simply subtract the principal from the total amount:

I=A−P=13620−12000=$ 1620I=A-P=13620 -12000 = \boxed{\$\ 1620}I=A−P=13620−12000=$ 1620​

Therefore, after 18 months, Amanda must pay $1620 more than the original amount of the loan.

Practice: Simple Interest
Calculate the total amount of an investment of $3500 at 6.8%/a simple interest for the following time periods:

a) 35 weeks

b) 500 days

c) 99 months

a) Total amount (to the nearest dollar) after 35 weeks

b) Total amount (to the nearest dollar) after 500 days

c) Total amount (to the nearest dollar) after 99 months

I don't know

Practice: Simple Interest
Terry takes out a loan for $7000 at 8.9%/a simple interest.
If Terry wants to ensure that the amount of interest paid does not exceed $500, what is the last day Terry can repay the loan?

Number of days so that total interest

\textbf{does not exceed}

$500:

I don't know

Practice: Simple Interest
Abdul forgets the amount of money he contributed to a new savings account on June 1, 2019. He earns simple interest, and his records (semi-annual) show the following balances in his account:

DateBalanceJan. 1, 2020$ 853.19Jun. 1, 2020$ 860.38Jan. 1, 2021$ 867.57\begin{array}{|c|c|}
\hline
\text{Date} & \text{Balance}\\
\hline
\text{Jan. 1, 2020} & \quad \$\ 853.19 \quad\\
\hline
\text{Jun. 1, 2020} & \$\ 860.38\\
\hline
\text{Jan. 1, 2021} & \$\ 867.57\\
\hline
\end{array}DateJan. 1, 2020Jun. 1, 2020Jan. 1, 2021​Balance$ 853.19$ 860.38$ 867.57​​

a) How much did Abdul contribute initially?

b) What is the annual interest rate for this savings account?

a) How much did Abdul contribute initially?

b) What is the annual interest rate (as a percentage) for this savings account?

I don't know