How can you determine the percentage of principal and interest from the first and last payment of a loan?

To determine the percentage of principal and interest from the first and last payment of a loan, the correct approach involves calculating the proportion of the payments that go towards principal and interest.

When looking at the first payment, the majority of it will typically go towards interest because the outstanding balance is still at its highest. By taking the total payment amount and dividing it by the portion that goes towards interest, you can gain insight into the interest component of that payment. Conversely, to find out the proportion that reduces the principal balance, you would divide the amount of principal paid (in the first payment) by the total payment. Therefore, this method effectively captures how much of the payment is allocated towards each component—interest and principal.

At the end of the loan term, the situation reverses. More of the payment goes towards the principal as the interest component diminishes due to the falling balance. Again, using the total payment and breaking it down into the principal and interest components allows you to establish their respective percentages.

This approach aligns well with the fundamentals of loan amortization, where early payments consist largely of interest, and later payments finish off the principal balance. Such calculations help in understanding the overall cost of the loan as it progresses through its term, thus making option