A $257 comma 800 mortgage for
A $257 comma 800 mortgage for 30 years for a new home isobtained at the rate of 7.8% compounded monthly. Find (a) themonthly payment, (b) the interest in the first payment, (c) theprincipal repaid in the first payment, and (d) the financecharge. (a) The monthly payment on the mortgage is $ nothing.(Round the final answer to two decimal places as needed. Round allintermediate values to six decimal places as needed.) (b) Theinterest in the first payment is $ nothing. (Round the finalanswer to two decimal places as needed. Round all intermediatevalues to six decimal places as needed.) (c) The principal repaidin the first payment is $ nothing. (Round the final answer to twodecimal places as needed. Round all intermediate values to sixdecimal places as needed.) (d) The finance charge is $nothing.
Answer:
According to given information principal amount P = $257800
Interest rate r =7.8% = 7.8/100 = 0.078
Compounding frequency is monthly so r = 0.078/12 = 0.0065
Now number of payments t = 30 x 12 = 360
Now we can use the below formula to find the payment (PMT)
PMT = [ p x r x (1+r)t ] / [(1+r)t-1]
PMT = [257800 x 0.0065 x (1+0.005)360 ] /[(1+0.0065)360-1]
PMT = [1675.7 x (1.0065)360/ [(1.0065)360– 1]
PMT = [1675.7 x 10.302924] / [10.302924 – 1]
PMT = [17264.609746] / [9.302924]
PMT = $1855.826162 ~ $1855.83
- So the monthly payment= $1855.83
- Interest for the first payment
Principal amount x 0.0065 = 257800 x0.0065 = $1675.7
- The principal repaid in the first payment
Monthly PMT – interest amount= 1855.83 – 1675.7 = $180.13
- Total finance charge can be calculated as
Finance charge = total payment– principal amount
Total payment = number ofpayments x PMT = 360 x 1855.83 = $668098.8
Now finance charge = 668098.8– 257800 = 410298.8
So finance charge =$410298.8
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