A homebuyer borrows 400,000 to be repaid over a 20 year period with level monthly payments beginning one month after the loan is made. The interest rate on the loan is a nominal annual rate of 12% convertible monthly. Find using mathematical formulas:
a. the total principal paid on the loan over the first 15 years
b. the total interest paid on the loan over the first 15 years
monthly payment or PMT formula
=PV/((1-(1+(r/m))^(-n*m))/(r/m))
=400000/((1-(1+(12%/12))^(-20*12))/(12%/12))
=4404.3445
a.
value of the loan at the end of 15 years=PMT*((1-(1+(r/m))^(-n*m))/(r/m))
=4404.3445*((1-(1+(12%/12))^(-5*12))/(12%/12))
=197997.48
the total principal paid on the loan over the first 15 years=loan amount-value of the loan at the end of 15 years
=400000-197997.48
=202002.52
b. the total interest paid on the loan over the first 15 years
=amount payment in 15 years-the total principal paid on the loan over the first 15 years
=(4404.3445*15*12)-202002.52
=590779.50
the above is answer..
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