Question

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%

Answer 1

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

$A=P\frac{i(1+i)^n}{(1+i)^n-1}$

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:

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

So the monthly payment is $117.81.

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

$A\cdot(12n)=117.81\cdot108=12723.48$

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

$I=12723.48-8400=4323.48$

So the total interest is $4323.48.