How to Calculate Interest Rate on a Loan
Stated bank loan interest rates give us a basis for comparing the cost of loan products. For example, which is the better of the two: a loan with 50% interest or 10%? The logical choice is the 10% loan.
If you’re a risky borrower, expect higher bank loan rates, and vice versa is true. For instance, prime borrowers on average pay about 10% on a personal loan from a traditional lender, while bad credit borrowers are charged rates ranging from 20% to 36%. That much we understand.
Now, when banks advertise loans like on their website, they might state the interest rate. The Truth in Lending Act requires them to tell you the APR, which is a true reflection of the cost of the loan. It’s sometimes called the Effective Annual Interest Rate, and you’ll see how it’s calculated, and how it differs from the stated interest rate.
Stated Interest Rate Defined?
SAR, in short, is the interest rate on the loan for an entire year expressed as a percentage. It’s very easy to calculate the cost of the loan because the SAR does not factor in compounding.
Let’s see a quick example:
Assuming you obtain a $5,500 loan for one year, and at the end of the term, the lender requires $5,800 to be repaid. What’s the SAR?
Simple Interest Rate Formula
Interest(I) = Principal (P) rate (r) time (t)
Interest = $5,800 – $5,500 = $300.
$300 = $5,500 x r x (12/12)
(300/5500) = r
0.0545 = r then r x 100% we get 5.45%.
For a simple interest loan, there is no compounding. Here, the SAR is equal to the effective interest rate.
Effective Annual Interest Rate (EAR)
If you’re looking forward to learning how to calculate interest rate on a loan, it’s important to note that the effective rate is always higher than the simple or stated rate. Compounding is also a vital concept to grasp.
On a simple loan, the interest rate is charged on the principal. So a 13.5% interest on a $450 loan will yield a finance charge of $60.75. Compounding allows interest to accumulate in periods. These periods can be semi-annually (2), quarterly (4), monthly (12), or daily (365). Here is an example to illustrate how to calculate interest on a loan:
A bank lends $11,250 to Peter with a SAR of 20% for 12 months. If the loan is a simple interest loan, Peter will repay $13,500, because:
I = $11,250×0.20 X (12/12)
I = $2,250
A = $2,250 +$11,250 = $13,500
You can also use this simple interest loan calculator.
The loan officer figures out that it’s better to compound the loan quarterly since it may lead to a better ROI. What is the EAR if the nominal rate was 20%?
We divide the interest by 4 periods to get the rate charged for each quarter.
20% ÷ 4 = 5%
Charge 5% on $11,250
$11,250 X 1.05 = $11,812.5
$11,812.5 X 1.05 = $12,403.125
$12,403.125 X 1.05 = $13,023.281
$13,023.281×1.05 = $13,674.445
Are you surprised that compounding results in more interest? Well, that’s because the real interest is more than the stated bank interest rate.
Real Interest Rate Formula
EAR = [1 + (SAR ÷ Compounding period) ^ Periods] – 1
Finding the brackets first:
EAR = [1 + (0.20 ÷ 4)^4]- 1
Step 1 = (1 + 0.05) ^ 4 = 1.2155 – 1 = 0.2155
Step 2 = Let’s multiply this by the loan principal, we get an interest amount of 0.2155 x $11,250 = $2,424.375
Adding to $2,424.375, the total payment is $13,674.375 and EAR is 21.55%.
Comparing EAR for Two Loan Products:
Which of these loans would you choose?
|Loan A||Loan B|
|Term||1 year||1 year|
Finding the EAR:
1) EAR = (1 + 0.105/2) ^ 2 – 1 X 100% = 10.7756%.
2) EAR = (1 + 0.104/4) ^ 4 – 1 X 100% = 10.8126%
Now based on this comparison, it’s clear that compounding can have a significant influence on the interest amount. Loan A had a higher SAR but it ended up being cheaper because it had fewer compounding periods.
Effective Loan Interest Rates Calculated for Loans with Different Features
Next, we’re going to find the real interest rates for a discount loan, compensating balance loan, and an installment loan.
1. Discounted Loans – Effective Interest Rate Calculation
For discounted loans, the lender first calculates the interest amount and deducts it from the principal. The balance is what is availed to the borrower. When the loan due date comes around, the lender requires you to pay the full loan amount before the interest was taken out. It can be quite confusing when described, so let’s go over one example.
John borrows $5,000 for 2 years at 8%. He has to repay the bank $5,000. What is the EAR for this discount loan?
Step 1: Calculate the finance charge based on the simple interest formula and deduct it from the loan principal.
I = Prt
Interest = $5,000 x (0.08) x 2
The interest is $800. It’s referred to as the discount, hence the name discounted loan.
Subtracting it from the principal means John receives $4,200 in his account.
The EAR for the discount loan is given by the formula:
A = P (1+rt)
A = Final amount paid
P = Principal (In essence, he received $4,200, but not $5,000 as expected)
r = annual interest percentage
t = number of years
$5,000 = $4,200 (1 + r(2))
(5,000/4,200) – 1 = 2r
r = 0.09523
EAR is given as a percentage = 9.523%
The EAR as expected happens to exceed the SAR.
2. Loans with Compensating Balances
When a bank asks you to open an account with them and deposit some cash prior to approving your loan, you might be dealing with a loan with a compensating balance. Banks may invest the cash you deposited and claim all the proceeds. The compensating balance is usually expressed as a percentage of the total loan amount.
Company Y takes out a $100,000 loan at a rate of 10%. The compensating balance is also 10%. Find the EAR of the loan.
EAR = (Principal amount X r) ÷ (Principal – Compensating balance)
= ($100,000×0.01) ÷ ($100,000 – $10,000)
= 0.1111 stated as a percentage is 11.11%
With this formula, you may not need to know the principal to figure out the EAR.
EAR = (Stated interest or SAR) ÷ (1- c)
c- Compensating balance percentage
= (10%) ÷ (1-0.1)
How to calculate bank interest for installment loans
Installment loans have one identifying characteristic. You make equal repayments that may be weekly, biweekly, or monthly.
Mary borrows an installment loan of $1,000 for 2 years at 12%. Using an interest calculator loan, there will be 24 payments of $47.07 and total interest is $130.
You can also find the payment amount manually using the following formula:
Monthly Payment = P (r(1+r)^n) ÷ ((1+r)^n-1).
Payments = 1,000 (0.012 (1+ 0.012) ^ 24) ÷ ((1 + 0.012) ^24)-1)
= $1,000 X ((0.012 (1.3314)/(0.3314))
= $ 48.21
There are various formulas for finding the EAR for installment loans:
1. Actuarial method
It’s the preferred method employed by banks. But, it’s difficult for the average loan customer to use it because it has complicated formulas. You can, however, find a loan interest calculator online that uses the actuarial method. The results you’ll get will be far more accurate than other formulas discussed here.
It gives the closest value to the actuarial method. Its formula is:
Effective Interest = (M X C X (95 X N + 9)) ÷ (12 X N X (N + 1) X (4PC + C))
3. Constant – Ratio
It has all parameters used for the N-ratio formula. And it’s much simpler.
Effective Annual Interest Rate = 2 x M x C ÷ (P x (N + 1))
|M||It’s the annual number of payments|
|C||Finance charge – the total cost of a loan|
|N||Total number of payments – until loan term ends|
- Using N-Ratio:
The loan amount is $1000, term 2 years, finance charge ($130 interest + $20 fees) = $150.
EAR = [12 X 150 X (95 X 24 + 9)] ÷ [12 X 24 X 25 X (4X1,000 + $150)]
= 4120200 ÷ 117129600
= 0.1378 or 13.78%
- Using Constant-Ratio
= [2 X 12 X 150] /[1000×25]
= 3,600 ÷ 25,000
= 0.144 or 14.4%
Basically, you’ll have no problem when you calculate interest on loan with fixed monthly payments by using these two formulas.
What is the average bank interest rate?
Banks have interest rates for savings accounts of which they average at 0.1% or 0.09%. The interest rate for bank loans ranges from 5% to 36%, but some banks have rates starting from 3%.