Westley Finch buys a house in Conshohocken for 275000 He mak

Westley Finch buys a house in Conshohocken for $275,000. He makes a 20% down payment (so that he does not have to pay any mortgage insurance) and then he finances the remaining balance with a 25 year mortgage in which he will make equal payments at the end of each month. The annual interest rate is 2.4% and interest is compounded monthly.

(a) What regular payment must Westley make at the end of each month in order to ammortize his loan?

(b) Assuming that Westley makes all of his payments on time, how much interest does Westley pay?

(c) After making 10 years of payments, Westley wins the Powerball lottery. (Woohoo!) He decides to immediately pay off his remaining balance in one lump sum. What is the amount of this payment?

Solution

a) HEre 20% of 275,000 = 275,000 x 0.20 = 55000 that is paid as downpayment.

So total amount remaining to pay as loan in 25 years is 275,000 - 55000 = $220,000

Now we have monthly payment formula given as :

Monthly payment = [rate +{rate/[(1+rate)^month)-1]}] x principal

Here payment is 220,000 rate is 2.4/1200 =0.002 ( as there are 12 months in a year)

and total months are 25 x 12 = 300 months

So monthly payment = [0.002 +{0.002/[(1+0.002)^300)-1]}] x 220,000

= [0.002 +{0.002/[(1.002)^300)-1]}] x 220,000= [0.002 +{0.002/([(1.002)^300)-1]}] x 220,000

= [0.002+{0.002/(1.821-1)}] x 220,000=[0.024 +(0.002/0.821)] x 220,000

=(0.002+0.002436) x 220,000 = 0.004436 x 220,000 =976

so monthly payment will be $ 976 Answer

b) so total payment including interest = 976 x 300 =$ 292,800

so Westley pays total interest = $292,800 - ^220,000 = $ 72,800 Answer

c) Now as there are 10 x 12 = 120 months in 10 years

so at the rate of $976 per month, he had already paid 976 x 120 = $117,120 in 10 years

so total amount to pay remaining = $220,000 - $ 117,120 = $102,880

   Answer