Jasmine is taking out a small business loan for her floral shop. She plans to apply for a $30,000 loan with a 5-year term and a 3.75% interest rate. She is unsure of her expected monthly profits, so she wants to know the benefit of a smaller loan. Using the loan amortization formula, how much money would Jasmine save over the life of the loan if she were to borrow $10,000 less?

Question

Jasmine is taking out a small business loan for her floral shop. She plans to apply for a $30,000 loan with a 5-year term and a 3.75% interest rate. She is unsure of her expected monthly profits, so she wants to know the benefit of a smaller loan. Using the loan amortization formula, how much money would Jasmine save over the life of the loan if she were to borrow $10,000 less?

Answer 1

To calculate the benefit of a smaller loan, we can use the loan amortization formula. The formula can be written as:

A = P * [r * (1 + r)^n] / [(1 + r)^n - 1]

Where:
A = monthly payment
P = loan amount
r = monthly interest rate (annual rate divided by 12)
n = total number of payments (number of years multiplied by 12)

In this case, let's start by calculating the monthly payment for the original loan of $30,000 with a 5-year term (60 months) and a 3.75% interest rate.

First, we need to calculate the monthly interest rate:
r = 3.75 / 100 / 12 = 0.003125

Next, let's calculate the monthly payment:
A = 30000 * [0.003125 * (1 + 0.003125)^60] / [(1 + 0.003125)^60 - 1]

Calculating this equation will give us the monthly payment for the original loan.

Now, let's calculate the monthly payment for a loan that is $10,000 less, so the loan amount would be $20,000.

Using the same formula, we can plug in the new loan amount of $20,000 and calculate the new monthly payment.

Finally, to find the savings over the life of the loan, we can subtract the new monthly payment from the original monthly payment and multiply the result by the total number of payments (60 months in this case).

Here is the step-by-step process to calculate the savings:

1. Calculate the monthly payment for the original loan of $30,000.
2. Calculate the monthly payment for a loan of $20,000 (which is $10,000 less).
3. Subtract the new monthly payment from the original monthly payment.
4. Multiply the difference in monthly payments by the total number of payments (60 months).
5. The result will be the savings over the life of the loan if Jasmine were to borrow $10,000 less.

Please note that the exact savings will depend on the specific loan terms and interest rates.