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liberstina [14]
3 years ago
14

Consider a home mortgage of ​$225,000 at a fixed APR of 4.5 ​% for 30 years. a. Calculate the monthly payment. b. Determine the

total amount paid over the term of the loan. c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.
Mathematics
1 answer:
White raven [17]3 years ago
4 0

<u>The formula for the monthly payment</u>.....

M= \frac{P(1+r)^nr}{[(1+r)^n] -1} , where P = the principal amount, r = the monthly interest rate and n = the total number of months.

Here annual interest rate is given as 4.5%

So, the monthly interest rate =\frac{4.5\%}{12}= 0.375\% = 0.00375

Total number of months = (30*12)months=360 months

Also given that, the principal amount is $225000

a.  So, the monthly payment will be.....

M= \frac{P(1+r)^nr}{[(1+r)^n] -1}\\ \\ M= \frac{225000(1+0.00375)^3^6^0*0.00375}{(1+0.00375)^3^6^0 -1}\\ \\ M= \frac{225000(1.00375)^3^6^0*0.00375}{(1.00375)^3^6^0 -1} \\ \\ M \approx 1140

Thus, the monthly payment will be approximately $1140


b. The <u>total amount paid</u> over the term of the loan will be: \$ 1140*360 months = \$ 410400


c.   As the principal amount was $225000 , so the amount of interest = (\$ 410400- \$ 225000)= \$ 185400

So, the percentage of amount that is paid toward the principal =\frac{225000}{410400}*100\% =54.82\%

and the percentage of amount that is paid toward the interest =\frac{185400}{410400}*100\%=45.18\%

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