Question

Tyrell bought a house for $186,500. He has a 30 year mortgage with a fixed rate of 6.5%. Tyrell’s monthly payments are $1,060.93. How much was Tyrell’s down payment?
a.
$12,120
b.
$18,650
c.
$27,975
d.
$37,300

Answer 1

Let r = 0.065/12 = 0.0054166667 (monthly rate) and n = 30·12 = 360. For a loan amount L, monthly payment M satisfies
M = L·[r / (1 − (1+r)^{-n})].

So
L = M·(1 − (1+r)^{-n})/r
≈ 1060.93·(1 − (1.0054166667)^{-360})/0.0054166667
≈ $167,850 (approx).

Down payment = 186,500 − 167,850 ≈ $18,650.

Answer: b.