– WELCOME TO AN EXAMPLE OF DETERMINING THE MONTHLY LOAN

PAYMENT FOR A MORTGAGE. THE PRICE OF A HOME IS $155,000. THE REQUIRED DOWN PAYMENT IS 10% AND YOU QUALIFY FOR A 30 YEAR

FIXED MORTGAGE AT 5.5%. NUMBER ONE, WE WANT TO DETERMINE

THE DOWN PAYMENT AND THE LOAN AMOUNT. NUMBER TWO, WE WANT TO FIND

THE MONTHLY MORTGAGE PAYMENT, AND, NUMBER THREE, DETERMINE

HOW MUCH INTEREST IS PAID OVER THE LIFE OF THE LOAN. SO FOR NUMBER ONE, SINCE THE

DOWN PAYMENT REQUIREMENT IS 10%, WE WANT TO FIND 10% OF 155,000. SO THAT WOULD BE 155,000 x 10%

EXPRESSED AS A DECIMAL, WHICH WOULD BE 0.10

OR, IF WE WANT, JUST 0.1. THIS WOULD BE $15,500. OF COURSE, IF WE WANT TO CHECK

THIS WE CAN USE A CALCULATOR, 155,000 x 0.1 OR 0.10=$15,500. SO IF THIS IS THE DOWN PAYMENT

THEN THE LOAN AMOUNT IS EQUAL TO THE PRICE OF THE

HOME 155,000 – THE DOWN PAYMENT, SO THIS WOULD GIVE US $139,500. THIS WOULD BE THE LOAN AMOUNT. AND NOW FOR NUMBER TWO WE WANT TO FIND THE MONTHLY

MORTGAGE PAYMENT. TO DO THIS BY HAND WE’LL BE

USING THIS FORMULA HERE. I’LL ALSO SHOW HOW TO USE

THE TI84 GRAPHING CALCULATOR TO DETERMINE

THE MONTHLY PAYMENT. SO FIRST USING OUR FORMULA, THE MONTHLY PAYMENT IS GOING TO

BE EQUAL TO THIS QUOTIENT HERE WHERE P IS THE LOAN AMOUNT

OF 139,500 x R DIVIDED BY N WHERE R IS THE ANNUAL INTEREST

RATE AND N IS THE NUMBER OF PAYMENTS

PER YEAR. SO R IS 5.5%, EXPRESSED AS

A DECIMAL THAT WOULD BE 0.055. OR MAKING MONTHLY PAYMENTS, SINCE THERE’S 12 MONTHS

IN A YEAR N IS 12 DIVIDED BY 1 – THE

QUANTITY 1 + R DIVIDED BY N, WHICH, AGAIN, IS 0.055

DIVIDED BY 12 RAISED TO THE POWER OF -N x T,

WHICH IS -12 x T, WHICH IS TIME IN YEARS. THIS IS A 30 YEAR FIXED MORTGAGE

SO T IS 30. AND NOW WE’LL GO

TO THE CALCULATOR. LET’S EVALUATE THE NUMERATOR AND

DENOMINATOR SEPARATELY FIRST. SO FOR THE NUMERATOR WE’LL HAVE

139,500 x 0.055 DIVIDED BY 12. SO THE NUMERATOR IS 639.375. AND NOW FOR THE DENOMINATOR

WE’LL HAVE 1 – THE QUANTITY 1 + 0.055 DIVIDED BY 12 RAISED TO

THE POWER OF THIS WOULD BE -360, AND ENTER. SO WE HAVE APPROXIMATELY

0.80722. AND NOW WE’LL GO AHEAD

AND FIND THIS QUOTIENT. SO THE MONTHLY PAYMENT IS GOING

TO BE APPROXIMATELY $792.07. KEEP IN MIND, THIS DOES NOT

INCLUDE TAXES AND INSURANCE. LET’S ALSO VERIFY THIS USING THE FINANCE MENU

OF THE GRAPHING CALCULATOR. SO WE’RE GOING TO PRESS APPS,

ENTER FOR FINANCE, AND THEN ENTER FOR TMV SOLVER. N IS THE NUMBER OF PAYMENTS

IN THE LOAN THAT WOULD BE 30 x 12 OR 360. THE INTEREST RATE IS 5.5%. EV IS THE PRESENT VALUE

OF THE LOAN, WHICH IS THE LOAN AMOUNT

OF $139,500. WE’LL COME BACK TO THE PAYMENT. THE FUTURE VALUE WOULD BE 0

AFTER THE LOAN IS PAID. PAYMENTS PER YEAR IS 12, NUMBER OF COMPOUNDS PER YEAR

IS ALSO 12. PAYMENTS ARE MADE

AT THE END OF THE MONTH. SO NOW WE’LL GO BACK UP TO PMT

FOR PAYMENT. WE’RE GOING TO CLEAR THIS AND NOW WE’RE GOING

TO PRESS ALPHA, ENTER FOR SOLVE. SO ALPHA, ENTER, VERIFIES THAT

OUR MONTHLY PAYMENT WOULD BE $792.07 ROUNDED

TO THE NEAREST CENT. REMEMBER WE ALSO ROUNDED

OUR DENOMINATOR HERE. AND NOW FOR THE LAST QUESTION

WE’RE GOING TO DETERMINE HOW MUCH INTEREST IS PAID

OVER THE LIFE OF THE LOAN. LET’S FIRST DETERMINE THE AMOUNT

PAID OVER THE LIFE OF THE LOAN. THAT WOULD BE THE MONTHLY

PAYMENT, WHICH IS $792.07 x THE NUMBER

OF MONTHS OVER 30 YEARS. SO THIS WOULD BE x 30 x 12. SO WE HAVE $792.07 x 360,

OR IF WE WANT 30 x 12, SO OVER 30 YEARS A TOTAL

OF $285,145.20 WILL BE PAID. WELL, REMEMBER THE LOAN AMOUNT,

OR THE AMOUNT BORROWED, WAS $139,500. SO THE DIFFERENCE OF THESE

TWO AMOUNTS WOULD BE THE AMOUNT OF INTEREST

PAID. SO WE’LL GO AHEAD AND TAKE

THIS AMOUNT HERE AND SUBTRACT THE LOAN AMOUNT

$139,500. SO $145,645.20 IS THE AMOUNT OF

INTEREST PAID OVER THE 30 YEARS. NOTICE THE AMOUNT OF INTEREST

PAID IS ACTUALLY MORE THAN

THE ORIGINAL LOAN AMOUNT. I HOPE YOU FOUND THIS EXAMPLE

HELPFUL. THE NEXT EXAMPLE WE’LL TAKE

A LOOK AT A LOAN THAT ALSO HAS POINTS.

## 8 comments

## OpenMindedSal

Wow! I Found What I Was Looking For!…Thank You

## Doris Magri

Hi Math, you are clear for showing us your maths of mortage payment. I like your video and the explanation you have a good calculator. I would try to see your video's they are very good

## Reddwin

holy cow, thank you.

## Abhilash Scariya

Very good. Thank you.

## Outdoors Nevada

Do a 15 year mortgage.

## Erica Mitchell

Thank you sooooo much very helpful

## Elizabeth Troncoso

Thank you sooo much. VERY VERY helpful

## Jay S

Wow thx. Its great that you decided to make a vid on this. I'll have to watch this about 30 more times though, lol. Every adult that has loan responsibilities should watch and learn if they dont know already. I'm a subscriber now. I hope u have more basic and problem solving financial math vids on ur channel.