Answer:
(a)$5805.21
(b)Least Expensive Mortgage =$120640.59
Most Expensive Mortgage =$152032.77
Step-by-step explanation:
The future value of an ordinary annuity with deposits P made regularly k times each year for n years, with interest compounded times k per year at an annual rate r, is given as:
![F.V.=\dfrac{P[(1+i)^{kn}-1]}{i}](https://tex.z-dn.net/?f=F.V.%3D%5Cdfrac%7BP%5B%281%2Bi%29%5E%7Bkn%7D-1%5D%7D%7Bi%7D)
The Pirerra's Monthly Payments=$140
Annual Rate =9.5%
Therefore: Monthly Rate=0.095/12
Years, n=3
Period, k=12
![F.V.=\dfrac{140[(1+\frac{0.095}{12} )^{3*12}-1]}{\frac{0.095}{12} }=\$5805.21](https://tex.z-dn.net/?f=F.V.%3D%5Cdfrac%7B140%5B%281%2B%5Cfrac%7B0.095%7D%7B12%7D%20%29%5E%7B3%2A12%7D-1%5D%7D%7B%5Cfrac%7B0.095%7D%7B12%7D%20%7D%3D%5C%245805.21)
(b)For the Johnsons, Present value of Mortgage is derived using the formula:
![\Text{Present Lump Sum}, A_0=\dfrac{P[1-(1+i)^{-kt}]}{\frac{r}{k} }](https://tex.z-dn.net/?f=%5CText%7BPresent%20Lump%20Sum%7D%2C%20A_0%3D%5Cdfrac%7BP%5B1-%281%2Bi%29%5E%7B-kt%7D%5D%7D%7B%5Cfrac%7Br%7D%7Bk%7D%20%7D)
At $1000 Monthly payment
![\Text{Present Lump Sum}, A_0=\dfrac{1000[1-(1+\frac{0.08}{12} )^{-12*15}]}{\frac{0.08}{12} }=\$104640.59](https://tex.z-dn.net/?f=%5CText%7BPresent%20Lump%20Sum%7D%2C%20A_0%3D%5Cdfrac%7B1000%5B1-%281%2B%5Cfrac%7B0.08%7D%7B12%7D%20%29%5E%7B-12%2A15%7D%5D%7D%7B%5Cfrac%7B0.08%7D%7B12%7D%20%7D%3D%5C%24104640.59)
Adding a down payment of $16000
- Least Expensive Mortgage = 104640.59+16000=$120640.59
At $1300 Monthly Payment
![\Text{Present Lump Sum}, A_0=\dfrac{1300[1-(1+\frac{0.08}{12} )^{-12*15}]}{\frac{0.08}{12} }=\$136032.77](https://tex.z-dn.net/?f=%5CText%7BPresent%20Lump%20Sum%7D%2C%20A_0%3D%5Cdfrac%7B1300%5B1-%281%2B%5Cfrac%7B0.08%7D%7B12%7D%20%29%5E%7B-12%2A15%7D%5D%7D%7B%5Cfrac%7B0.08%7D%7B12%7D%20%7D%3D%5C%24136032.77)
Adding a down payment of $16000
- Most Expensive Mortgage = 136032.77+16000=$152032.77
$21.50(40) + $31.88 (62-40)
$21.50(40) + $31.88(22)
$860 + $701.36
$1561.36
Answer: I would say that x = 10 degrees
Step-by-step explanation:
The angle has a square, meaning it is a right angle. Right angles are 90 degrees, and you're given 80 degrees + x.
90 - 80 = 10
Hope this helps!
Answer:
r=20
Step-by-step explanation:
to get rid of the division part, you multiply 6 each side. now you have r+10=30. to solve, now you subtract 10 from both sides. this gives you r=20 :)
Look at all the options... the correct one should have a
negative slope (so it would be a line decreasing), and it should also
intersect on the Y axis at 2.