The interest rate plays a crucial role in the calculation of a fully amortizing payment. A fully amortizing payment refers to a periodic payment made towards a loan that includes both principal and interest, ensuring that the loan is completely paid off by the end of its term. The interest rate directly affects the amount of interest paid over the life of the loan and, consequently, the size of the fully amortizing payment.
When determining the fully amortizing payment, the interest rate is used to calculate the interest portion of each payment. The interest portion is based on the outstanding loan balance and the interest rate. In general, a higher interest rate will result in a larger interest portion of the payment, while a lower interest rate will lead to a smaller interest portion.
To illustrate this, let's consider an example. Suppose you have a $100,000 loan with a 5% annual interest rate and a 30-year term. To calculate the fully amortizing payment, you would divide the loan amount by the present value
factor of an ordinary annuity, which takes into account the interest rate and the loan term.
The present value factor of an ordinary annuity is derived from a mathematical formula that considers the interest rate and the number of periods. In this case, with a 5% interest rate and a 30-year term, the present value factor is approximately 17.9088.
Using this factor, you can calculate the fully amortizing payment as follows:
Fully Amortizing Payment = Loan Amount / Present Value Factor
= $100,000 / 17.9088
Therefore, in this example, the fully amortizing payment would be approximately $5,582.42 per month.
Now, let's consider how the interest rate impacts this calculation. If we increase the interest rate to 6%, while keeping all other factors constant, the present value factor decreases to approximately 16.2816. Using the same loan amount, the fully amortizing payment would now be:
Fully Amortizing Payment = $100,000 / 16.2816
As you can see, the higher interest rate results in a larger fully amortizing payment. This is because a higher interest rate increases the cost of borrowing, leading to a greater amount of interest that needs to be paid off over the loan term.
Conversely, if we decrease the interest rate to 4%, the present value factor increases to approximately 19.8493. Using the same loan amount, the fully amortizing payment would now be:
Fully Amortizing Payment = $100,000 / 19.8493
In this case, the lower interest rate leads to a smaller fully amortizing payment.
In summary, the interest rate directly impacts the calculation of a fully amortizing payment. A higher interest rate results in a larger fully amortizing payment, while a lower interest rate leads to a smaller fully amortizing payment. It is important to consider the interest rate when determining the affordability and overall cost of a loan.