Respuesta :
It is $99.04 more per month.
The payment is calculated by P = A/D, where A is the amount of the loan and D is the discount factor.
D = (((1+r)^n)-1)/(r(1+r)^n), where r is the annual interest rate as a decimal divided by 12, and n is the number of months he will be paying.
Since the rate is 9.1%, r = (9.1/100)/12 = 0.091/12 = 0.0076
For the 25 year loan, n = 25*12 = 300:
D = (((1+0.0076)^300)-1)/(0.0076(1+0.0076)^300) = 118.004
P = A/D = 165000/118.004 = 1398.26 per month
For the 20 year loan, n = 20*12 = 240:
D = (((1+0.0076)^240)-1)/(0.0076(1+0.0076)^240) = 110.198
P = A/D = 165000/110.198 = 1497.30 per month
The difference between payments is
1497.30 - 1398.26 = 99.04
The payment is calculated by P = A/D, where A is the amount of the loan and D is the discount factor.
D = (((1+r)^n)-1)/(r(1+r)^n), where r is the annual interest rate as a decimal divided by 12, and n is the number of months he will be paying.
Since the rate is 9.1%, r = (9.1/100)/12 = 0.091/12 = 0.0076
For the 25 year loan, n = 25*12 = 300:
D = (((1+0.0076)^300)-1)/(0.0076(1+0.0076)^300) = 118.004
P = A/D = 165000/118.004 = 1398.26 per month
For the 20 year loan, n = 20*12 = 240:
D = (((1+0.0076)^240)-1)/(0.0076(1+0.0076)^240) = 110.198
P = A/D = 165000/110.198 = 1497.30 per month
The difference between payments is
1497.30 - 1398.26 = 99.04
Answer:
The difference between the monthly payments is [tex]\$99.18[/tex]
Step-by-step explanation:
We know that,
[tex]\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right][/tex]
Where,
PV = Present value of annuity,
P = payment per period,
r = rate of interest per period,
n = number of period.
Monthly payment for 25 years.
[tex]\Rightarrow 165000=P\left[\dfrac{1-(1+\frac{0.091}{12})^{-25\times 12}}{\frac{0.091}{12}}\right][/tex]
[tex]\Rightarrow P=\dfrac{165000}{\left[\dfrac{1-(1+\frac{0.091}{12})^{-300}}{\frac{0.091}{12}}\right]}=\$1395.99[/tex]
Monthly payment for 20 years.
[tex]\Rightarrow 165000=P\left[\dfrac{1-(1+\frac{0.091}{12})^{-20\times 12}}{\frac{0.091}{12}}\right][/tex]
[tex]\Rightarrow P=\dfrac{165000}{\left[\dfrac{1-(1+\frac{0.091}{12})^{-240}}{\frac{0.091}{12}}\right]}=\$1495.17[/tex]
Therefore, the difference between the monthly payments is [tex]1495.17-1395.99=\$99.18[/tex]
