9.05 Loans
While borrowing money can be useful for buying things that we can't currently afford, it's not a free service. A loan is a service that allows you to borrow money and then repay that over time, plus a bit extra.
This extra amount is called interest which is calculated as a percentage of the amount that needs to be repaid.
Simple interest
Simple interest is calculated as a flat percentage of the amount that was borrowed.
We can calculate the simple interest of a loan using the formula:
$I=Prn$I=Prn
Where $I$I is the interest accumulated, $P$P is the principal amount borrowed, $r$r is the rate of interest per period and $n$n is the number of periods.
Repaying loans
When repaying loans, calculations are required so that the number of repayments and the size of a repayment multiply to match the total amount to be repaid.
The total amount to be repaid on a loan is equal to the sum of the principal amount borrowed and the total interest accumulated.
$\text{Total amount }=\text{Principal amount }+\text{Interest accrued}$Total amount =Principal amount +Interest accrued
$\text{Total amount }=\text{No. repayments}\times\text{Size of repayments}$Total amount =No. repayments×Size of repayments
Since the 'total amount' appears in both equations, we can relate the number and size of repayments to the principal amount and interest. As such, knowing any three of these values will allow us to find the fourth.
Practice questions
Question 1
What is the total interest to be paid on a $2$2-year $\$3000$$3000 loan at $17%$17% p.a. flat interest?
Question 2
The simple interest on a loan of $\$6600$$6600 over $33$33 months is $\$1252.35$$1252.35.
If the annual interest rate is $R$R, find $R$R as a percentage to the nearest one decimal place.
Enter each line working as an equation.
Question 3
Katrina takes out a loan to purchase a surround sound system. She makes $19$19 equal loan repayments. The total loan amount paid is $\$95000$$95000.
What is the value of each repayment?