Loan is the money one borrows from a friend, a bank, or another financial organization in return for reimbursement of the capital plus interest in the future. The amount borrowed is termed as the principal while the interest is the fee you paid to get the loan. Because creditors are taking a chance that you may default on the loan, they must compensate for this risk by collecting a fee known as interest. Secured and unsecured loans are the most common types of loans. A secured loan is one in which the borrower pledges an item (like a car, boat, or house) as security.
Loan Balance
Banks and creditors often provide convenient repayment methods such as monthly installments, whereby the debtors would reimburse the lender with equal amounts every month until the debt is finished. The quantity of a debt that still has to be paid is referred to as the loan balance. It is calculated by deducting the total of all preceding principal payments from the total loan amount.
The formula for loan balance is given as follows:
where,
B is the balance to be paid,
A refers to the principal,
P is the payment made,
r is the compounded rate of interest and
n is the number of time periods.
Sample Problems
Question 1. What would be the balance loan amount after 1 year if the principal amount is $10000, monthly payment being $200 and an annual interest rate of 5%.
Solution:
Given: A = $10000, P = $200, r = 2% or 5/1200 = 0.0041, n = 1 year = 12 months
Let the balance loan amount after one year be B.
As per the loan balance formula,
. Substituting the given values in the formula, we have:
B =
= 10000(1.0503) − 48780.48(1.0503 − 1)
= 10503 − 2453.658
= $ 8049.34
Question 2. What would be the balance loan amount after 1 year if the principal amount is $20000, monthly payment being $200 and an annual interest rate of 5%.
Solution:
Given: A = $20000, P = $200, r = 2% or 5/1200 = 0.0041, n = 1 year = 12 months
Let the balance loan amount after one year be B.
As per the loan balance formula, B =
. Substituting the given values in the formula, we have:
B =
= 20000(1.0503) − 48780.48(1.0503 − 1)
= 21006 − 2453.658
= $ 18552.342
Question 3. What would be the balance loan amount after 1 year if the principal amount is $30000, monthly payment being $200 and an annual interest rate of 5%.
Solution:
Given: A = $30000, P = $200, r = 2% or 5/1200 = 0.0041, n = 1 year = 12 months
Let the balance loan amount after one year be B.
As per the loan balance formula,
. Substituting the given values in the formula, we have:
= 30000(1.0503) − 48780.48(1.0503 − 1)
= 31509 − 2453.658
= $ 29055.342
Question 4. What would be the balance loan amount after 1 year if the principal amount is $40000, monthly payment being $200 and an annual interest rate of 5%.
Solution:
Given: A = $40000, P = $200, r = 2% or 5/1200 = 0.0041, n = 1 year = 12 months
Let the balance loan amount after one year be B.
As per the loan balance formula,
. Substituting the given values in the formula, we have:
B =
= 40000(1.0503) − 48780.48(1.0503 − 1)
= 42012 − 2453.658
= $ 39558.34
Question 5. What would be the balance loan amount after 1 year if the principal amount is $50000, monthly payment being $200 and an annual interest rate of 5%.
Solution:
Given: A = $50000, P = $200, r = 2% or 5/1200 = 0.0041, n = 1 year = 12 months
Let the balance loan amount after one year be B.
As per the loan balance formula,
Substituting the given values in the formula, we have:
B =
= 50000(1.0503) − 48780.48(1.0503 − 1)
= 52515 − 2453.658
= $ 50061.342
Question 6. What would be the balance loan amount after 1 year if the principal amount is $60000, monthly payment being $200 and an annual interest rate of 5%.
Solution:
Given: A = $60000, P = $200, r = 2% or 5/1200 = 0.0041, n = 1 year = 12 months
Let the balance loan amount after one year be B.
As per the loan balance formula,
Substituting the given values in the formula, we have:
B =
= 60000(1.0503) − 48780.48(1.0503 − 1)
= 63018 − 2453.658
= $ 60564.342
Question 7. What would be the balance loan amount after 1 year if the principal amount is $70000, monthly payment being $200 and an annual interest rate of 5%.
Solution:
Given: A = $70000, P = $200, r = 2% or 5/1200 = 0.0041, n = 1 year = 12 months
Let the balance loan amount after one year be B.
As per the loan balance formula,
. Substituting the given values in the formula, we have:
B =
= 70000(1.0503) − 48780.48(1.0503 − 1)
= 73521 − 2453.658
= $ 71067.342