Question

Vanessa bought a house for $268,500. She has a 30 year mortgage with a fixed rate of 6.25%. Vanessa’s monthly payments are $1,595.85. How much was Vanessa’s down payment?
a. $9,314.45
b. $16,781.25
c. $40,275.00
d. $53,040.00

Answer 1

Answer:

Her down payment was $9,314.45

Step-by-step explanation:

We know that,

$\Rightarrow \text{Original price}=\text{Down payment}+\text{Present value of annuity}$

$\Rightarrow \text{Down payment}=\text{Original price}-\text{Present value of annuity}$

And

$\text{PV of annuity}=P[\dfrac{1-(1+r)^{-n}}{r}]$

Here,

P = Payment = $1,595.85 per monthly

r = Rate of interest = 6.25% annually = 0.0625 annually = $\dfrac{0.0625}{12}$ monthly

n = Number of period = 30 years = 360 months

Putting the values,

$\text{PV of annuity}=1598.85[\dfrac{1-(1+\dfrac{0.0625}{12})^{-360}}{\dfrac{0.0625}{12}}]\\\\=\ 259,185.55$

So,

$\Rightarrow \text{Down payment}=268,500-259,185.55=\ 9,314.45$