Question

eter wants to buy a duplex with a purchase price of $226,950. Peter can afford a 10% down payment. Peter earns $2,985 a month and wants to spend no more than 10% of his income on his mortgage payment. Peter is going to rent out the other half of the duplex. He thinks that if he charges $900 a month in rent this will cover the remainder of his mortgage payment. Given that Peter has a 30 year mortgage with a fixed rate of 6.25%, how should Peter adjust how much he charges for rent of the other half of the duplex?
a.
Peter should increase the rent by $200.
b.
Peter should increase the rent by $60.
c.
Peter should increase the rent by $10.
d.
Peter should keep the rent at $900.

Answer 1

Loan = 226,950 - 10% = 226,950 - 22,695 = 204,255.

Monthly rate r = 6.25%/12 = 0.0052083333, n = 360.
Monthly mortgage payment M = P * r / (1 - (1+r)^-n) ≈ $1,258 (about $1,257.8).

Peter will pay at most 10% of $2,985 = $298.50 himself, so required rent ≈ 1,257.8 - 298.5 ≈ $959.3.

He planned $900, so he should increase the rent by about $59.3 ≈ $60.

Answer: b.