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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

Verified Answer :

InesWalston

Answer:

Her down payment was $9,314.45

Step-by-step explanation:

We know that,

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And

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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,

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

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