Morgan is buying a house for $314,000. She is financing $275,000 and obtained 25-year, fixed-rate mortgage with 5.875% interest rate. How much are er monthly payments?
A) $24,272.20
B)$21,296.15
C)$1,999.18
D)$1,754.06

Question

Morgan is buying  a house for $314,000. She is financing $275,000 and obtained  25-year, fixed-rate mortgage with 5.875% interest rate. How much are er monthly payments? 
A) $24,272.20
B)$21,296.15
C)$1,999.18
D)$1,754.06

tkhunny · Answer

Reasonableness - No Interest: 275000 / (25*12) = 275000 / 300 = 917  --  Okay, it will have to be greater than that, but not an order of magnitude greater.  I think this rules out A and B.

Generally, 

i = 0.05875 -- The annual interest rate.
j = i/12 = 0.004895833... -- The monthly interest rate.
v = 1/(1+j) = 0.995128019 -- The monthly discount factor.

After that, it's a matter of basic principles.

$275000 = Pmt\cdot (v + v^{2} + ... + v^{300}) = Pmt\cdot\dfrac{v-v^{301}}{1-v}$

Thus,

$Pmt = 275000\dfrac{1-v}{v-v^{301}} = 1750.88$

Well, it's not quite one of the answers, but a little rounding difference can cause that with a mortgage of this size.

Keeping 6 decimal places throughout, 

j = 0.004896
v = 0.995128
Pmt: 1750.88

That didn't help much.  Just 4 decimal places?

j = 0.0049
v = 0.9951
Pmt: 1756.56

Whoops!  Too far.  Then 5 decimal places?

j = 0.00490
v = 0.99512
Pmt: 1752.51

What I seem to be saying is that rounding is important.