## anonymous one year ago Please help! Need it urgently! Will fan and medal! Madison is financing $382,300 to purchase a house. How much money will she save over the life of a 30 year, fixed rate loan by buying 3 points with a rate of 5.13% instead of not buying points with a rate of 5.88%? Round to the nearest dollar$60,948 $63,242$53,302

1. anonymous

@mathmate can you help me? I think it's $63,242 but I'm not sure. . 2. mathmate First, it is important to understand what is meant by "buying 3 points". Each point reduces the interest rate by 0.25%, so 5.88% becomes 5.13% after buying three points. The actual amount paid for each point is irrelevant here. 3. mathmate If you chose$63242, how much did you get for the monthly payment at each interest rate?

4. anonymous

For the 5.88% interest rate I got $374 for monthly payments for 30 years 5. anonymous For the 5.13% I got$345 for monthly payments for 30 years

6. mathmate

I'm not sure $345 is right.$345*30 years *12months/year = 124200 which is not even one third of the money borrowed.

7. anonymous

This is the calculator I used :/ https://www.creditkarma.com/calculators/amortization

8. anonymous

@mathmate do you know a formula I can use or can you walk me through it please?

9. mathmate

The calculator is correct, but don't know what numbers you put in: Principal is 382300 interest is 5.88% p.a. (or 5.13% p.a.) # of years is 30. I do not get $345. Can you try it again? After that, we can look at formulas. 10. anonymous Ah I see! Sorry, I think I put the 63,242 instead of 382,300 :/ Okay so using the 5.88% interest rate, the monthly payments are$2,263. And the 5.14% interest rate gives a monthly payment of 2,083

11. mathmate

A few corrections: 1. the interest rates are 5.88% and 5.13% 2. I do not get any of the given answers, even though one of them is closer to mine. Can you check if the principal is indeed 382300, and not for example 373300?

12. anonymous

The principal is $382,300. I used the interest rate 5.13% but didn't check before I sent it to you but I did use 5.13 not 5.14. 13. anonymous It shows me that the Monthly Principal & Interest is$2,083 for 5.13%

14. mathmate

The answer is then the difference, and multiplied by 360 months, or (2263-2083)*360 which gives $64800. A more accurate calculation can be done using formulas: Let A=amount borrowed P=monthly payment R=1+monthly interest n=number of months Then P=$$\Large \frac{AR^n*(R-1)}{R^n-1}$$ which gives monthly payments of$2262.67 and $2082.75 respectively. Over 30 years, the difference is$64771.45

15. mathmate

I am not able to reproduce exactly any of the give answers. If your teacher shows you a way to do that, please post the explanations.

16. anonymous

No he hasn't given us any formulas or anything to find the answer, that's why I needed help. But thank you so much for your help and your patience!

17. mathmate

no problem! Please use the formula to check my calculations. Let me know if you find anything wrong.