Monthly Loan Repayment Formula

Question

I need a layman's explanation on how to calculate monthly loan repayments. I don't know algebra.

To calculate the monthly repayment on £3000 with an APR of 7.9% over 10 years I'm doing the following: 3000 * 0.079 * 10 + 3000 / 120 = Monthly repayment of £44.75 & total repayable £5370

When I use an online loan calculator, £3000 with an APR of 7.9% over 10 years has a monthly repayment of £35.85 and total repayable £4297.28

Where am I going wrong with my maths? P.S Maths isn't exactly one of my strong points so a simple idiot proof explanation would be appreciated. Thanks.

Answer 1

Usually the calculation is at follows. Two assumptions:

• Monthly constant repayments ($x$)
• Duration: 120 months
• APR: 0.079
• Payments are made at the end of each month.

Then the equation is

$$3000\cdot \left(1+\frac{0.079}{12}\right)^{120}= x\cdot \frac{\left(1+\frac{0.079}{12}\right)^{120}-1}{\frac{0.079}{12}}$$

$$x=3000\cdot \left(1+\frac{0.079}{12}\right)^{120}\cdot \frac{0.079}{ 12\cdot \left( \left(1+\frac{0.079}{12}\right)^{120}-1 \right)}$$

Solve the equation for $x$ (repayment). The calculator gets $x=36.24$

See the pictures of the parts of the table from this site. All numbers can be comprehended. There is no mystery about the numbers.

Table(1), Table(2), Table(3) ,Table(4), Table(5)

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Example: Interest and principal in march 2021:

• Balance in february 2021: $2916.46$

• Interest in march 2021: $2916.46\cdot \frac{0.079}{12}=19.200...\approx 19.20$

• Principal in march 2021: $36.24-19.20=17.04$

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In general the payment can be made at the beginning at each month as well. Then the equation is

$$3000\cdot \left(1+\frac{0.079}{12}\right)^{120}= x\cdot \color{blue}{\left(1+\frac{0.079}{12}\right)}\cdot \frac{\left(1+\frac{0.079}{12}\right)^{120}-1}{\frac{0.079}{12}}$$

The calculator gets $x=36.00$

Answer 2

$\displaystyle{\tt @Anon2945}$: $\displaystyle\color{red}{\tt java script}$ is $\displaystyle\underline{\it fine}$ !!!.

// Filename: js23sep2020.js
// Run as node js23sep2020.js
"use strict";
const c0 = 3000, n = 120, r = 7.9/1200;
const MONTHLYPAYMENT= c0*r/(1.0 - Math.pow(1.0 + r,-n));

console.log("MONTHLY PAYMENT = " + MONTHLYPAYMENT);

$\displaystyle\tt \mathrm{MONTHLY\,\,\, PAYMENT} = 36.23995171985522$.