The total interest paid on a 3-year loan at 6% interest compounded monthly is $1085.16. Determine the monthly payment for the loan. (Please explain using formulas and broken down each step instead of what to input in a calculator. Thank you)
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Answer:The monthly payment is $361.72.Step-by-step explanation:Given : The total interest paid on a 3-year loan at 6% interest compounded monthly is $1085.16. To find : Determine the monthly payment for the loan?Solution : The total interest paid on a 3-year loan compounded monthly is $1085.16. i.e. [tex]36M-P=1085.16[/tex] ....(1)Where, M is the monthly paymentP is the principal.3 year loan = [tex]3\times 12=36[/tex] months.We know, The monthly payment formula is [tex]M=P\times\frac{i}{1-(1+i)^{-t}}[/tex]Here, The value of P is [tex]P=\frac{(1-(1+i)^{-t})M}{i}[/tex]Where, i is the interest rate monthly [tex]i=\frac{6}{1200}=0.005[/tex]t is the time monthly [tex]3\times 12=36[/tex] monthsSubstitute in (1),[tex]36M-\frac{(1-(1+i)^{-t})M}{i}=1085.16[/tex][tex]M(36-\frac{(1-(1+i)^{-t})}{i})=1085.16[/tex][tex]M(36-\frac{(1-(1+0.005)^{-36})}{0.005})=1085.16[/tex][tex]M(36-\frac{(1-(1.005)^{-36})}{0.005})=1085.16[/tex] [tex]M(36-\frac{(1-0.835)}{0.005})=1085.16[/tex] [tex]M(36-\frac{0.165}{0.005})=1085.16[/tex] [tex]M(36-33)=1085.16[/tex] [tex]M(3)=1085.16[/tex] [tex]M=\frac{1085.16}{3}[/tex] [tex]M=361.72[/tex] Therefore, The monthly payment is $361.72.