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

Her down payment was $9,314.45

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[(1-(1+r)^(-n))/(r)]`

Here,

P = Payment = $1,595.85 per monthly

r = Rate of interest = 6.25% annually = 0.0625 annually =
`(0.0625)/(12)` monthly

n = Number of period = 30 years = 360 months

Putting the values,

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

So,

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