homework: payout annuity or loans formula score: 83.34/100 answered: 9/10 question 7 you decide to quit…

Explanation:

Step1: Convert annual - interest rate to monthly - interest rate

The annual interest rate $r = 16.55%=0.1655$. The monthly interest rate $i=\frac{r}{12}=\frac{0.1655}{12}$.

Step2: Calculate the number of payments

The loan is to be paid off in 3 years. Since the payments are made monthly, the number of payments $n = 3\times12=36$.

Step3: Use the present - value of an annuity formula

The present - value of an annuity formula is $PV = PMT\times\frac{1-(1 + i)^{-n}}{i}$, where $PV$ is the present value of the loan (balance), $PMT$ is the monthly payment. We know that $PV=$12900$, $i=\frac{0.1655}{12}$, and $n = 36$. We need to solve for $PMT$. First, rewrite the formula for $PMT$: $PMT=\frac{PV\times i}{1-(1 + i)^{-n}}$. Substitute the values: $i=\frac{0.1655}{12}\approx0.013792$ $(1 + i)^{-n}=(1 + 0.013792)^{-36}$ Using a calculator, $(1 + 0.013792)^{-36}\approx0.6177$ $1-(1 + i)^{-n}=1 - 0.6177 = 0.3823$ $PV\times i=12900\times0.013792\approx177.82$ $PMT=\frac{177.82}{0.3823}\approx465.13$

Step4: Calculate the monthly interest payment

The monthly interest payment on the outstanding balance in the first month is based on the initial balance. The monthly interest rate $i=\frac{0.1655}{12}\approx0.013792$. The initial balance is $PV = 12900$. The monthly interest payment $I=12900\times0.013792\approx177.82$

Answer:

The monthly interest payment is approximately $$177.82$ and the monthly payment is approximately $$465.13$