Use the appropriate amortization formula to find (a) the monthly (n=12) payment on a loan with the given conditions and (b) the total interest that will be paid during the term of the loan.$8,400 is amortized over 9 years at an interest rate of 9.9%

Respuesta :

a) In order to calculate the monthly payment for the amortization, we can use the formula:

[tex]A=P\frac{i(1+i)^n}{(1+i)^n-1}[/tex]

Where A is the periodic payment amount, P is the principal amount, i is the interest rate and n is the total number of payments.

Since we have monthly payments, we can multiply the value of n (initially we have n = 9) by 12 and divide the interest rate by 12, so we have:

[tex]\begin{gathered} A=8400\frac{\frac{0.099}{12}(1+\frac{0.099}{12})^{9\cdot12}}{(1+\frac{0.099}{12})^{9\cdot12}-1} \\ A=8400\frac{0.00825\cdot2.42867}{2.42867-1} \\ A=117.81 \end{gathered}[/tex]

So the monthly payment is $117.81.

b) First let's calculate the total value paid:

[tex]A\cdot(12n)=117.81\cdot108=12723.48[/tex]

Now, subtracting from the principal, we have the interest:

[tex]I=12723.48-8400=4323.48[/tex]

So the total interest is $4323.48.

ACCESS MORE
EDU ACCESS