Question

1. find the monthly interest payment, amount applied to the principle, and the new balance for the first month for the simple interest installment loan. $500 financed 6 monthly payments $87.02 monthly payment 15% annual rate $1200 financed 6 monthly payments $207.06 monthly payment 12% annual rate

Explanation:

First Loan ($500, 6 months, $87.02 payment, 15% annual rate)

Step1: Calculate monthly interest rate

The annual interest rate is 15%, so the monthly interest rate $r$ is $\frac{15\%}{12}= 0.0125$.

Step2: Calculate monthly interest

Using the simple - interest formula for the first month (principal $P = 500$), the monthly interest $I$ is $I=P\times r=500\times0.0125 = 6.25$.

Step3: Calculate amount applied to principal

The monthly payment is $87.02$. The amount applied to principal $A$ is the monthly payment minus the monthly interest, so $A = 87.02-6.25=80.77$.

Step4: Calculate new balance

The new balance $B$ is the original principal minus the amount applied to principal, so $B = 500 - 80.77 = 419.23$.

Second Loan ($1200, 6 months, $207.06 payment, 12% annual rate)

Step1: Calculate monthly interest rate

The annual interest rate is 12%, so the monthly interest rate $r$ is $\frac{12\%}{12}=0.01$.

Step2: Calculate monthly interest

Using the simple - interest formula for the first month (principal $P = 1200$), the monthly interest $I$ is $I = P\times r=1200\times0.01 = 12$.

Step3: Calculate amount applied to principal

The monthly payment is $207.06$. The amount applied to principal $A$ is the monthly payment minus the monthly interest, so $A=207.06 - 12=195.06$.

Step4: Calculate new balance

The new balance $B$ is the original principal minus the amount applied to principal, so $B = 1200-195.06 = 1004.94$.

Answer:

• For the $500 loan:
• Monthly interest: $\$6.25$
• Amount applied to principal: $\$80.77$
• New balance: $\$419.23$
• For the $1200 loan:
• Monthly interest: $\$12$
• Amount applied to principal: $\$195.06$
• New balance: $\$1004.94$