# Monthly, Quarterly, and Yearly Loan Repayment Calculator

This monthly, quarterly, and yearly **loan repayment calculator** can help businesses, entrepreneurs, or the average Joe, break down the payments of a loan based on interest rate, the length of the loan, and additional payment options.

Loans can affect a company valuation, and lead to a higher calculated business valuation if leveraged correctly. Therefore, it is important to look at the numbers closely, understand the ins and outs of a loan repayment schedule, and how interest rates can change your payments.

## Table of Contents

## Loan Repayment Calculator

Monthly Payment: $0

## Input Needed For The Loan Repayment Calculator

**Loan Amount ($)**: The total amount of the loan (e.g. 100000).**Annual Interest Rate (%)**: The interest rate of the loan (e.g. 12).**Loan Term (in months)**: Length of the loan, in months (e.g. 60 = 5 years).**Payment Frequency**: How often are payments made? Monthly? Quarterly? Annually?**Extra Monthly Payments ($)**: Extra payments, above the minimum, added each term.**One Off Extra Payment ($)**: If instead (or in addition) there is a one-off extra payment, on top of the minimum.**Month for One Off Extra Payment**: What month is the one-off extra payment done? (e.g. 12, means that on the 12th month there was an extra payment added)

## When or Why To Use the Monthly, Quarterly, and Yearly Loan Repayment Calculator

Quite often in Shark Tank, the Sharks offer loans instead of making a straight investment. That’s the case when there is a higher risk. From the investment standpoint, it may be safer and more cautious to loan the money, rather than exchange them for a percentage of equity.

When that happens, here you can calculate the payout time and see how it changes based on the payment schedule. You can also add one off extra payments, or recurring extra payments. I developed it this way to keep some flexibility in the payoff schedule.

## How Does The Amortization Formula Work? (for the nerds)

The formula used by the monthly, quarterly, or yearly loan repayment calculator, known as the loan amortization formula, is given by:

Where:

- [math] M [/math] is the total monthly payment.
- [math] P [/math] is the principal loan amount (the initial loan balance).
- [math] r [/math] is the monthly interest rate (annual interest rate divided by 12).This is adapted to the schedule if it’s done quarterly or annually
- [math] n [/math] is the total number of payments (adjusted for monthly, quarterly, annual)

### Breakdown of the Formula

- [math]P \times r[/math]: This part calculates the interest amount for one period (month). It’s the product of the principal amount and the monthly interest rate
- [math]1 + r[/math]: This calculates the growth factor per period. Adding 1 to the monthly interest rate accounts for both the principal and the interest in the repayment.
- [math](1 + r)^{-n}[/math]: This part discounts the future value of the loan to its present value. Raising the growth factor to the power of (-n) (the total number of payments) calculates the present value of all future payments
- [math]\frac{P \times r}{1 – (1 + r)^{-n}}[/math]: Finally, the monthly payment (M) is calculated by dividing the interest amount for one period by the present value factor. This gives the fixed monthly payment amount that will pay off the loan over the term, including both principal and interest.

## Practical Example for the Monthly, Quarterly, Yearly Loan Repayment Calculator

Let’s say you have a loan amount of $100,000 [math](P)[/math], an annual interest rate of 6% [math](annual\ rate = 0.06)[/math], so [math](r = 0.06 / 12 = 0.005)[/math], and a term of 30 years [math](n = 30 \times 12 = 360) months[/math].

Plugging these values into the formula gives:

- [math] M = \frac{100,000 \times 0.005}{1 – (1 + 0.005)^{-360}} [/math]
- [math] M = \frac{500}{1 – (1.005)^{-360}} [/math]
- [math] M = \frac{500}{1 – 0.174110…} [/math]
- [math] M = \frac{500}{0.825889…} [/math]
- [math] M \approx 605.03 [/math]

So, the monthly payment [math](M)[/math] would be approximately $605.03.

This formula ensures that the loan is paid off exactly by the end of the term, with the payment covering both the interest and principal over the course of the loan.