What is the Annual Interest Rate?
We often come across instances of transactions involving loans, bank deposits, installments and lending or borrowing money. All these instances involve the role of interest and a principal amount. Let us learn about these two concepts in a little more detail.
- Interest is the amount of money earned or paid when lending or borrowing money. The amount that is borrowed or lent is called the principal amount.
- Simple interest is the interest only on the principal amount.
The annual interest rate is defined as the simple interest paid or received annually and is expressed as a percentage of the principal amount. The annual interest rate, simple interest and principal amount are related by the formula:
I = Prt
Where,
I = Simple interest
P = Principal
r = Annual interest rate (expressed in decimal form)
t = Time (in years)
We can use this formula to calculate the annual interest rate to solve problems on simple interest.
Rapid Recall
I = Prt
Here, I = Simple interest, P = Principal, r = Annual interest rate (expressed in decimal form), and t = Time (in years)
Solved Examples
Example 1: Robyn has decided to deposit $400 in her bank account. She will earn $18 simple interest in 12 months. Find the annual interest rate.
Solution:
I = Prt [Formula for simple interest]
18 = 400(r)(1) [Substituting the values for I, P and t]
18 = 400r [Simplify]
0.045 = r [Dividing both sides by 400]
Hence, Robin deposited the money in the bank at an annual interest rate of 0.045 or 4.5%.
Example 2: Angelica is purchasing a car priced at $16,000 and has taken a loan to pay for the car. If the simple interest amount that she has to pay is $4,800 for 5 years, find the annual interest rate.
Solution:
I = Prt [Formula for simple interest]
4800 = 16000(r)(5) [Substitute for I, P and t]
4800 = 80000r [Multiply]
0.06 = r [Dividing both sides by 80000]
Hence, the annual rate of interest for the car is 0.06 or 6%.
Example 3: Find the annual rate of interest if the principal amount is $2000, the time is 18 months, and the interest amount is $210.
Solution:
Find the annual interest rate using the formula, I = Prt
First, we will express the given time in years. For that, we will divide the number of months by 12,that is,
\(\frac{18}{12}= \frac{3}{2} = 1\text{ }\frac{1}{2}=1.5\) years
Now, substitute the values in the formula.
210 = 2000(r)(1.5)
210 = 3000r [Multiply]
0.07 = r [Dividing both sides by 3000]
Hence, the annual rate of interest is 0.07 or 7%.
The principal amount is the amount that was initially borrowed or lent. It is denoted by ‘P’.
Simple interest is defined as the interest amount that is paid only on the principal amount. It is denoted by ‘I’, and is given by the formula, I = Prt, where, ‘P’ is the principal, ‘r’ is the interest rate and ‘t’ is the period of time the principal amount is lent or borrowed.
Learning about simple interest and its uses will give us an improved understanding of how loans function. This will help us in the future while making monetary decisions.
The total of principal and interest leads to the balance amount that one has to pay after a certain period of time.