#### PV = L * (1 – (1+r)^{-n} / r)

- PV is the present value of Outstanding Balance
- L is the existing Payment
- r is the rate of interest
- n is the frequency of payments

## Debt Payoff Calculator

Debt Payoff calculator is a type of calculator wherein if the borrower wishes to consolidate the outstanding loans and try to pay them off quickly to reduce the interest burden and excess amount outflow.

### About Debt Payoff Calculator

First, find out the present value of the outstanding balances on the multiple loans.

**PV = L * (1 – (1+i)**

^{-n}/ r)Next would be to find out the new instalment amount, which could be either sum of existing instalment amount and additional payment if any to be made.

Now calculate the period within which the debt can be paid off

**nPVA = ln ((1 – PV(i) / L’)**

^{-1)}) / ln (1+i)Wherein,

- PV is the present value of Outstanding Balance
- L is the existing Payment
- L’ is the new Payment
- i is the rate of interest
- n is the frequency of payments
- nPVA is the number of periodical payments

It is a handy calculator as it will calculate what will be the tenure when all the debts are paid off. In this case, the borrower can be sitting with multiple loans with different rates of interest and is willing to consolidate them. Further, the borrower could even wish to increase the instalment amount periodically or consolidate the instalment amount as well. This shall help him in reducing the interest burden and also clear off debt early. The decision is not as easy as it required to increase the instalment amount, which could increase the burden on the cash flow of the borrower. This calculator shall only help to calculate within what span of time they can pay off the debt entirely when the debts are consolidated.

### How to Calculate Using the Debt Payoff Calculator?

One needs to follow the below steps to calculate the tenure of consolidated debt pays off.

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

**Step #2 – **Now determine the new instalment amount, which is the sum of the existing instalment amount that he is currently paying and the additional amount that borrower is thinking to start with.

**Step #3 – **Find out the loan, which is higher interest-bearing and clear that debt pays off first and continues paying minimum or instalment amount for other outstanding loans.

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**Step #4 – **Now calculate the outstanding principal on the remaining loans and calculate the tenure of the loan with the new instalment amount.

**Step #5 – **The resultant tenure can be converted into years by dividing the value arrived in step 4 by 12 and figures on the right side of the decimal can be multiplied by 12 to get them in months.

### Example

Mr X has two loans outstanding one is an auto loan, and another one is a mortgage loan.

The details of both the loans are given below:

The branch Manager has approached Mr X with a scheme wherein he can consolidate the loans currently outstanding and can pay off debt early. The banker provided him scheme details which were to pay off the higher debt first and then continue the fixed amount of the closed loan to be repaid on the mortgage loan which shall reduce his tenure of loan closure. Mr X also agreed to increase the instalment amount by $200 while consolidating the outstanding loans and will continue to do so until the debts are paid off.

You are required to calculate the tenure by which Debt shall be paid off.

**Solution:**

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

**Auto Loan**

Rate of interest applicable on monthly basis = 8 / 12 = 0.67%

The remaining period will be (7 * 12) – (3 * 12) which is 84 – 36, that is 48.

**PV = L * (1 – (1+i)**

^{-n}/ r)- =$545. 52 * (1 – (1+0.67%)
^{-48})/ 0.67%) **=$22,345.54**

**Mortgage Loan**

Rate of interest applicable on monthly basis = 5 / 12 = 0.42%

The remaining period will be (25 * 12) – (10 * 12) which is 300 – 120 that is 180.

**PV = L * (1 – (1+i)**

^{-n}/ r)- = $1,227.64 *(1 – (1+0.42%)
^{-180}/ 0.42%) **= $155,241.51**

Consolidated outstanding loan

- = $22,345.44 + $155,241.40
**= $177,586.84**

We are given here, the existing monthly instalment that he is paying on an auto loan is $545.52, and existing instalment amount on a Mortgage loan is $1,227.64. Consolidated instalment amount would be $1,773.16, and further Mr X also wants to increase this amount by $200. Therefore, the total new instalment amount would be $1,973.16

First, the instalment amount of Auto loan would be paid off since its higher interest-bearing, and the new amount that would be used to pay off the auto loan would be $545.52+ $200 which is $745.52, and rest amount will be used to pay off Mortgage loan which is $1,973.16 – $745.52 that equals to $1,227.64

Now, we shall calculate within what span of time will Auto loan be cleared off

**nPVA = ln ((1 – PV(i) / L’)**

^{-1)})/ ln (1+i)- = ln (((1- 22,345.44 * (0.67%) / 745.52)
^{-1})/ ln (1+0.67%) **= 33.55**

Now outstanding tenure of Mortgage loan would be 180 less 33.55 which is 146.45

**Mortgage Loan After Auto Loan Is Paid Off**

Rate of interest applicable on monthly basis = 5 / 12 = 0.42%

**PV = L * (1 – (1+i)**

^{-n}/ r)- = $1,227.64 * (1 – (1+0.42%)
^{-146.45}/ 0.42%) **= $134,374.99**

Now, we shall calculate within what span of time will Mortgage loan be cleared off

**nPVA = ln ((1 – PV(i) / L’)**

^{-1})/ l*n*(1+i)- = ln (((1- 134,374.92 * (0.42%) / 1,973.16)
^{-1}) / ln (1+0.42%) **= 80.26**

Therefore, the total tenure within which loan can be cleared off is 33.55 + 80.26, which is 113.81 and when divide the same by 12 which is 9.48 years that is in 9 years and 6 months.

### Recommended Articles

This has been a guide to the Debt Payoff Calculator. Here we provide you with the calculator to find out the tenure when all the debts are paid off with some examples. You may also take a look at the following useful articles –