Respuesta :
Answer:
For the 30 year loan, the monthly payments will be of $1330.6.
For the 15 year loan, the monthly payments will be of $1797.66
Step-by-step explanation:
The formula for the monthly payment is given by:
[tex]M=P(\frac{i(1+i)^n}{(1+i)^n-1})[/tex]In which:
P is the principal(the price of the house).
i is the monthly interest rate.
n is the number of payments.
30 year loan:
$200,000 house, so P = 200,000.
Interest rate of 7%, YEARLY. So monthly, we have that i = 0.07/12.
Monthly payments for 30 years. Then n = 30*12 = 360. So the monthly payment is:
[tex]M=200000\ast(\frac{\frac{0.07}{12}(1+\frac{0.07}{12})^{360}}{(1+\frac{0.07}{12})^{360}-1})=1330.6[/tex]For the 30 year loan, the monthly payments will be of $1330.6.
15 year loan:
Now, the only thing that changes is the number of monthly payments.
15 years, each with 12 months. 15*12 = 180, so n = 180.
[tex]M=200000\ast(\frac{\frac{0.07}{12}(1+\frac{0.07}{12})^{180}}{(1+\frac{0.07}{12})^{180}-1})=1797.66[/tex]For the 15 year loan, the monthly payments will be of $1797.66
