# Loan Calculator With Extra Payments

## Loan Payments

Whenever we borrow money from a bank or an institution, we always arrange a payment plan afterward, to pay off the debt.

These payments are usually done monthly.

Each payment can usually be broken down into the following parts:

Payment Type | Explanation |
---|---|

Principal | This is the amount of money you borrowed from the bank, which will be deposited into your bank account once the loan is approved. |

APR/Interest | This is the official “cost” of the loan. Interest is the percentage value of your principal that will be paid from the leftover amount each year as an additional cost to your monthly payments. APR is essentially the same but includes some additional costs within it, such as origination fees, hence being a more relevant indicator in some countries, such as the USA. |

Extra Fees | Some additional fees may apply to loans. These are usually of a one-time origin, such as registration fees, or apply under certain conditions, such as late fees. |

Hence, each monthly payment consists of these parts. The larger our monthly payment is, the faster we can pay our loan off and the less total interest we pay.

## Calculating Monthly Payments

Figuring out your monthly payments can prove to be a very tedious task due to the sheer number of factors and extra payments that can be involved, alongside the regularly changing nature of your monthly payments, as they can change over time due to the lowered principal, changing interest rates, or extra fees.

It is always recommended to ask the bank directly for a breakdown of your payments or use an online calculator, such as this one.

We can offer a simplified formula for calculating your loan payments for each given year.

To work with it, you need the following variables.

Symbol | Explanation |
---|---|

P | The principal (the amount you borrowed and have left over to pay). |

r | The interest rate set up for your loan. |

n | Number of payments you make yearly (in the case of monthly payments, this value is 12). |

Y | Number of years you plan to pay the loan off for. |

Assuming your payments change yearly, the formula to calculate your monthly payments (M) is as follows:

M=\cfrac{P}{n*Y}+\cfrac{P*(\cfrac{r}{100*n})}{12}

After a year, you should calculate how much of your principal you already paid off, and then recalculate your monthly payment for the next year with the new, lowered principal, as well as the potentially new interest rate.

This formula also does not account for any extra fees or payments. Fixed monthly fees should be added to the sum at the end, while proportional fees (usually expressed as a percentage) should be added to the interest rate.

## Worked Out Example

Rob received a loan for $60,000 at a 6% interest rate. He has an origination and registration fee that totals $600, which he wants to pay off throughout the first year. He has no additional fees. His loan is set for 10 years. He will be making monthly payments.

His fees are recalculated yearly.

What is his monthly payment during the first and second years, assuming an unchanged interest rate?

*FIRST YEAR*

During the first year, Rob will pay his monthly fee with an additional 60012 = $50, to pay off the origination and registration fee.

We substitute P= 60,000, r = 6%, n = 12, and Y= 10 years.

M=\cfrac{P}{n*Y}+\cfrac{P*(\cfrac{r}{100*n})}{12}

=\cfrac{60,000}{12*10}+\cfrac{60,000*(\cfrac{6}{100*12})}{12}

=500+\cfrac{60,000*0.005}{12}

=500+\cfrac{300}{12}

=500+30=530

His monthly payment will be $500 for the principal, $30 for the interest, and $50 for the fees, totaling $580.

*SECOND YEAR*

During the second year, he would have paid 500×12 = $6,000 off of his principal. His new monthly payment will be calculated based on the new principal of $60,000-$6,000 = $54,000.

M=\cfrac{P}{n*Y}+\cfrac{P*(\cfrac{r}{100*n})}{12}

=\cfrac{54,000}{12*10}+\cfrac{54,000*(\cfrac{6}{100*12})}{12}

=450+\cfrac{54,000*0.005}{12}

=500+\cfrac{270}{12}

=450+22.5=475.5

During the second year, his monthly payment would be $450 for the principal, and $22.5 for the interest, totaling $475.5 a month.

In a real-life scenario, the banks use a variety of constants and other metrics to adjust the payments, hence these results are purely theoretical.