32. A house sells for $488,500 and a 30% down payment is made. A 30-year mortgag

Question

32. A house sells for $488,500 and a 30% down payment is made. A 30-year mortgage at 6.5% was obtained. Find the monthly payment and the total interest paid. MONTHLY PAYMENT PER $1000 ON MORTGAGE... ...(INCLUDES # OF YEARS) rate % 15 yrs 30 yrs 6.5 $8.71 $6.32 7 $8.99 $6.65 7.5 $9.28 $6.99 8 $9.56 $7.34 A) Monthly payment = $2,261.11; total interest paid = $472,049.60 B) Monthly payment = $2,161.12; total interest paid = $436,053.20 C) Monthly payment = $2,170.23; total interest paid = $439,332.80 D) Monthly payment = $2,152.97; total interest paid = $433,119.20

Explanation / Answer

The cost of the house is $ 488500 and the downpayment is 30 % of $ 488500 i.e. $146550. Therefore, the mortgage amount ( P) is $ 488500 - $ 146550 = $ 341950.

The formula for monthly payment ( M) is M = P[i(1+i)n] / [(1+i)n -1] . Here, i = r/12 where r is the rate of interest and n is the number of months for which mortgage has been taken.

Now r = 6.5 % or, 0.065. Therefore i = 0.065/12 = 0.054166667 (approx. on rounding off to 10 decimal places). Also, n = 30*12 = 360.

(1+i)n = ( 1 + 0.054166667)360 = 6.991796305;  i(1+i)n = 0.054166667* 6.991796305 = 0.03787223 ; (1+i)n -1 =  6.991796305 -1 =  5.991796305 . Therefore M =  341950.(0.03787223)/5.991796305 = $ 2161.36. The total amount repaid is M*360 = $ 2161.36*360 = $778089.60. Thus, the interest paid is $778089.60 - $ 341950 = $436139.6.

NOTE: We have done computations upto a maximumof 10 decimal places. If we compute upto more decimal places, the answer could undergo small changes. Of the possible answers given, B0 is closest to our computations.

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