The formula:
$699,000 * .80 = $559,200
Number of payments = 35 years x 12 months = 420 months
Interest rate as a decimal = 5% ÷ 100 = .005
Interest due on each payment = .05 ÷ 12 = 0.00416666666666666666666666666667
Payment = (0.00416666666666666666666666666667 * 559,200) / 1 – (1 + 0.00416666666666666666666666666667)^ - 420
= $2330.0000000000000000000000000019 / 0.82559311017996182684375136875003
= $2822.213474494850504974364179856
$2822.213474494850504974364179856 x 420 months - $559,200 =
$1,185,329.6592878372120892329555395 – $559,200 = $626,129.65928783721208923295553952
Therefore, Jen's total finance charges is $626,129.66
Answer:
$626,128.20
Step-by-step explanation:
Jen purchased a condo for $699,000. She put 20% down and financed the rest at 5% for 35 years.
The amount she made by down payment is,
[tex]=699,000\times \dfrac{20}{100}[/tex]
[tex]=\$139,800[/tex]
The amount left for monthly payment is,
[tex]=699,000-139,800=\$559,200[/tex]
We know that,
[tex]\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right][/tex]
Here,
PV = Present Value = $559,200,
P = Monthly payment,
r = Monthly rate of interest = [tex]\dfrac{0.05}{12}[/tex]
n = number of months = 35 years = 420 months
Putting the values,
[tex]\Rightarrow 559200=P\left[\dfrac{1-(1+\frac{0.05}{12})^{-420}}{\frac{0.05}{12}}\right][/tex]
[tex]\Rightarrow P=\dfrac{559200}{\left[\dfrac{1-(1+\frac{0.05}{12})^{-420}}{\frac{0.05}{12}}\right]}[/tex]
[tex]\Rightarrow P=\$2,822.21[/tex]
So total payment will be,
[tex]=139,800+(420\times 2,822.21)[/tex]
[tex]=\$1,325,128.2[/tex]
Therefore, the finance charge will be,
[tex]=1,325,128.2-699,000=\$626,128.20[/tex]
