harry took out a 25 - year loan for $160,000 at 9.6% interest, compounded monthly. if his monthly payment on…

harry took out a 25 - year loan for $160,000 at 9.6% interest, compounded monthly. if his monthly payment on the loan is $1409.05, how much of his first payment went toward note reduction?\n\na. $1280.00\nb. $135.27\nc. $1409.05\nd. $129.05

harry took out a 25 - year loan for $160,000 at 9.6% interest, compounded monthly. if his monthly payment on the loan is $1409.05, how much of his first payment went toward note reduction?\n\na. $1280.00\nb. $135.27\nc. $1409.05\nd. $129.05

Answer

Explanation:

Step1: Calculate monthly interest rate

Annual interest rate is 9.6%, so monthly interest rate $r=\frac{9.6%}{12}= 0.8%=0.008$.

Step2: Calculate interest portion of first - payment

The loan amount is $P = 160000$. Interest for the first month $I=P\times r=160000\times0.008 = 1280$.

Step3: Calculate note - reduction amount

Monthly payment is $M = 1409.05$. Note - reduction amount $=M - I=1409.05-1280=129.05$.

Answer:

D. $129.05$