## About Additional Payment Calculator

An additional Payment calculator is a type of calculator wherein the borrower can determine if they quick up their payments or start paying an additional amount periodically, then how much would they save and how their balance loan tenure shall be impacted.

The formula for calculating Additional Payment is not quite simple, and it requires certain steps per below:

**First, find out the present value of the outstanding balance on the loan**

**PV = P * [1 – (1+r)**

^{-n}/ r]**Next would be to find out the tenure with the new installment amount **

**nPVA = Ln [ (1 – PV(r) / P)**

^{-1}] / Ln (1+r)then, **nPVA x (Installment Amount + Additional Payment per Period)**

Wherein,

- FV is a future value of the balloon amount
- PV is the present value of Outstanding Balance
- P is the Payment
- P’ is the new Payment
- r is the rate of interest
- n is the frequency of payments
- nPVA is the number of periodical payments

The Additional Payment Calculator is very much useful to the borrower, especially when they are planning to increase their installment amount so that they save on interest payments and also pre-payment their loan early. This calculator shall help them to identify how much they shall save had they not made any additional payment. The borrower shall be able to determine whether his decision to make additional payment is worthwhile or not.

### How to Use the Additional Payment Calculator?

One needs to follow the below steps in order to calculate the monthly installment amounts.

**Step #1 – **First, a borrower needs to determine what is current loan outstanding balance, which is nothing but finding out the present value of the mortgage.

**Step #2 – **Now determine the new installment amount, which is the sum of the existing installment amount and the additional payment that the borrower is thinking to be made.

**Step #3 –** Use the nPVA formula to determine within what span of time the remaining loan would be paid off.

**Step #4 –** Multiply the nPVA calculated in step 3 by the new installment calculated in step 2.

**Step #5 –** Calculate the total value of installment already paid by multiplying the existing installment by a number of periods for which the same has been paid.

** Step #6 – **Take the sum of values arrived in step 4 and step 5, which shall be total outgo if additional payment is made.

**Step #7 – **Multiply the existing installment with a total number of periods.

**Step #8 – **Subtract Value arrived in step 7 by step 6, which shall yield the savings done by making additional payment.

### Example

Mrs. Yen Wen has taken a mortgage loan for $200,000 for a period of 30 years, and the rate of interest, which is applicable to the same, is 5%. Since she is an employee of the bank, she is eligible for a rebate on interest to the tune of 0.75%. Her monthly installment is $983.88 based on a current fixed rate. She would be eligible for promotion next year, and she is expecting a decent hike, and she feels that she would be able to increase the monthly installment by $200 and she feels that she would be able to save a substantial amount of interest and she would be able to close the loan earlier than current. It has been 4 years now since she has been paying the same installment every month, and she has not defaulted on any of the installments.

Based on the given information, you are required to calculate the savings she would make on her mortgage loan, and by what span can she expect to close the loan based on a new installment amount.

**Note:** You can ignore the time value of money since her additional payment starts from the end of year 5.

**Solution:**

We are given here; the existing monthly installment that she is paying is $983.88, which has to be paid until 30 years. Hence, here total outgo would if she continues to make the existing installment is $983.88 x 30 x 12, which is **$354,196.72**

Now, after 5 years, she wants to increase the monthly installment amount, which is $983.88 + $ 200, which equals **$1,183.88.**

We will now calculate what savings she shall make if this additional payment is made.

Rate of interest applicable on monthly basis = (5.00% – 0.75%) / 12 = 0.35%

The remaining period will be (30 * 12) – (5 * 12), which is 360 – 60, that is 300.

We need to calculate the present value of the current outstanding balance which can be calculated per below formula:

**PV = P * (1 – (1+r)**

^{-n}/ r)- = $983.88 * [1 – (1+0.35%)
^{-300}/ 0.35%] **= $181,615.43**

Now since we have the Present ValuePresent ValuePresent Value (PV) is the today's value of money you expect to get from future income. It is computed as the sum of future investment returns discounted at a certain rate of return expectation.read more of outstanding loan balance at the end of 5 years, we now need to Calculate the time period within which the loan can be close with the new installment amount.

^{-1}] / Ln (1+r)

- = Ln [ {(1- 181,615.43 x (0.35%) / 1,183.88}
^{-1}] / Ln (1+0.35%) **= 221.69**

Now we shall calculate the total outgo with new installment which is

New installment * nPVA i.e. 1,183.88 * 221.69 which equals to $262,454.13 and amount that is already paid which is $983.88 x 60 which is $59,032.80, and therefore the total amount paid under additional payment installment shall be $262,454.13 + $59,032.80 which is equal to $**321,486.93**

Therefore, savings on this additional payment will be $354,196.72 less $321,486.93 which is **$32,709.87.**

The number of periods of loan payment shall be reduced by 300 – 221.69, which is equal to **78.31** months, and in years it is 6 years and 6 months.

### Conclusion

The additional payment calculator, as discussed, is useful for the borrower to calculate the savings he can make by repaying the loan earlier that is through an additional amount added in every installment. This shall help in saving the interest as well as reducing the loan term.

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