Amortizing Loan Payments

Amortization refers to the separate calculation of amounts applied toward repaying a loan (the principal amount), and those applied to paying the interest incurred in taking out the loan, such that the loan is repaid at the end the term. DreamCalc will also calculate the remaining balance of the loan after the payments are made. Amortization is performed using the values stored in the TVM registers.

When the [AMORT] key is pressed, the current value in the display is taken to be the number of periodic intervals over which to amortize. The amount paid as interest is returned, and the amount paid toward the principal is placed in the K memory register. If you are working in RPN mode, the amount paid toward the principal is also placed in the Y stack register.

In addition, [AMORT] updates the Present Value (PV) register with the remaining balance and adds the number of periods amortized to the Number of Payments (n) register. Therefore, you can work forward to calculate the total principal and interest paid over any contiguous set of periods, and determine the remaining balance at the end of that time. Also, if you clear the Number of Payments register before amortizing, you can keep track of the number of periods amortized by recalling its value.

Examples

Example: Your bank offers you a loan of $15000 at an annual rate of 9.5% over 10 years, compounded monthly. In the first year, how much of the principal balance will you have paid off, how much interest will you have paid and what will be the remaining balance?

Step 1. To begin, ensure that the calculator is in the END payment mode and input the following data into the TVM registers as follows:

15000 [PV] (loan we receive)
10 [12×] (inputs 10 years of monthly payments to n register)
9.5 [12÷] (inputs monthly rate into i register*)
0 [FV] (loan repaid at end of term)

* European and Canadian users may use the EMR function to calculate the monthly rate.

Step 2. Now pressing [PMT] will give the repayment amount:

[PMT]
Displays: -194.10

Remember, this is negative because of the sign convention.

Step 3. Now we amortize the loan for the first 12 months:

12 [AMORT]
Displays: -1384.57 (the interest paid in the first year)

[X⇔Y] (this gives the Y stack value*)
Displays: -944.63 (the principal repaid in the first year)

[RCL] [PV] (recall the updated value in the PV register)
Displays: 14055.37 (the remaining balance)

* Algebraic users should recall the value in K register to retrieve the principal repaid.

Example: How much will be paid in interest on the loan above over the remaining 9 year period?

Remember, we can chain together amortization calculations. Continue from the above example, without reseting the calculator:

9
[ENTER]
12
[x] (9 years of montly repayments)
[AMORT]
Displays: -6906.70 (remaining interest to be paid)

In summary, the above loan would have cost $8291.27 (1384.57 + 6906.70) in total interest payments. Therefore, the total repaid would be $8291.27 plus the original loan amount (principal) of $15000, which is $23291.27.

Finally, to double check the calculation, the final amount may also be determined by simple multiplication of the monthly repayment by 10 x 12, which gives $194.10 x 120 = $23292.00. The small precision error, compared to the above figure, is expected and described below.

Rounding & Precision

The [AMORT] key internally rounds payment values to the display precision setting of the calculator. This will be especially applicable if you are using fixed precision and can lead to small rounding errors. The values shown in the above example assume a two digit fixed precision display. Other settings will yield slightly different result values. This is normal and is done to yield results close to those obtained by accounting techniques in general use.