#### Refinance New Installment

(P * R * (1+R)^{N*F} )/ ((1+R)^{N*F}-1)

- P is the outstanding loan balance
- R is the new rate of interest
- N is the number of periods for which the existing loan will continue
- F is the frequency with which the loan shall be repaid i.e. annually, semi-annually, monthly, etc.

## Refinance Calculator

A Refinance calculator is used to find the new instalment amount when the borrower refinances his loan with a new interest rate, and the same can be used to calculate the interest savings amount as well. This can be used to calculate for any loan which is issued on a reducing interest basis.

### About Refinance Calculator

First, we need to find out the outstanding principal balance just before the rate changes.

**Refinance New Installment = [P * R * (1+R)^N*F] / [(1+R)^N*F – 1]**

Wherein,

**P**is the outstanding loan balance.**R**is the new rate of interest.**N**is the number of periods for which the existing loan will continue.**F**is the frequency with which the loan shall be repaid, i.e. annually, semi-annually, monthly, etc.

There could be scenarios wherein the borrower has taken the loan during the business cycle when there is a high rate of interest prevailing in the market and further due to requirement at that moment the borrower could not wait further to delay the processing of a loan. Now, assume that the rate of interest has come down and the borrower wishes to refinance the loan at a lower rate of interest, and when he does the same, he would be saving the interest outflow which will reduce the cost of the purpose for which he had borrowed loan. When the borrower refinances at a lower rate of interest, the advantages would be reduced rate of interest, reduce instalment amount and also in certain cases the borrower can repay it sooner if that option is available to him. Hence, this calculator can be used to calculate the refinanced instalment amount and the savings amount.

### How to Calculate using Refinance Calculator?

One needs to follow the below steps –

**Step#1 –** First of all, one needs to determine the existing instalment, an initial loan taken, the number of years for which the loan was taken and the rate of interest.

**Step#2 – **There should be an option to the borrower to refinance the loan. Then we should calculate the outstanding balance of the loan if there was any repayment done in between and the same can be calculated using the table method as provided in the example below.

**Step#3 – **Now from above step2, determine the outstanding principal balance amount and also the remaining term of the loan (here we are assuming that the loan period will remain the same).

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**Step#4 – **Using the above formula, multiply the principal amount by a new rate of interest.

**Step#5 –** Continuing step4, compound the same by a new rate of interest.

**Step#6 –** As a final step, discount the result obtained in step 5 per formula discussed above, and that shall be a new instalment amount.

**Step#7 – **To determine the savings, one needs to calculate the difference between existing instalment and new instalment as calculated in step 6 and multiply the same with the remaining loan period.

### Refinance Calculator Example

Mr. Kedia had purchased a laptop for $13,500 with fully financed by Bank of Asia. The Bank has provided him with a loan for a period of 5 years with a reducing rate method. The rate of interest that will be charged by the bank is 13.50%, and the same was charged high because the credit score of Mr. Kedia was below par score. However, after paying the instalment for 2 years without any default, the credit score of Mr. Kedia improved, and the bank offered him to refinance his outstanding balance at 10.00% and to which Mr. Kedia agreed to. The existing instalment amount is $310.63 payable in 60 instalments.

Based on the given information, you are required to calculate the new periodical instalment for the remaining tenure and along with the savings that he would make.

**Solution:**

We will now summarize the information that we are given.

To calculate the new instalment amount, we are first required to calculate the outstanding balance of the loan borrowed and for the same calculation is below:

The monthly interest rate now will be 10.50% / 12 which is 0.83% and the outstanding balance of the loan as calculated above at the end of 2 years is 9,153.68 with a loan period of 3 years remaining which would be 36 months.

**At the end of 2 years**

**New EMI = [P * R * (1+R)^N*F] / [(1+R)^N*F – 1]**

- = [9,153.68 x 0.83% x (1 + 0.83%)^3×12 ] / [ (1 + 0.83%)^3×12 – 1 ]
**= 295.36**

**Savings Monthly = Existing Installment – New Installment**

- = 310.63 – 295.36
**= 15.27 per month**

**Total Savings During Remaining Period = Remaining Loan Period * Savings Per Month**

- = 36 * 15.27
**= 549.69**

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This has been a guide to the Refinance Calculator. Here we provide you with the calculator that finds the new instalment amount when the borrower refinances his loan with a new interest rate. You may also take a look at the following useful articles –