Answer:
Her down payment was $9,314.45
Step-by-step explanation:
We know that,
[tex]\Rightarrow \text{Original price}=\text{Down payment}+\text{Present value of annuity}[/tex]
[tex]\Rightarrow \text{Down payment}=\text{Original price}-\text{Present value of annuity}[/tex]
And
[tex]\text{PV of annuity}=P[\dfrac{1-(1+r)^{-n}}{r}][/tex]
Here,
P = Payment = $1,595.85 per monthly
r = Rate of interest = 6.25% annually = 0.0625 annually = [tex]\dfrac{0.0625}{12}[/tex] monthly
n = Number of period = 30 years = 360 months
Putting the values,
[tex]\text{PV of annuity}=1598.85[\dfrac{1-(1+\dfrac{0.0625}{12})^{-360}}{\dfrac{0.0625}{12}}]\\\\=\$259,185.55[/tex]
So,
[tex]\Rightarrow \text{Down payment}=268,500-259,185.55=\$9,314.45[/tex]
