Question

Peter 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

Answer: b. Increase the rent by $60.

Work:
- Down payment = 10% of $226,950 = $22,695 → loan = $226,950 − $22,695 = $204,255.
- Monthly rate = 6.25%/12 = 0.0052083333, n = 360.
- Monthly mortgage ≈ 204,255 * [r / (1 − (1+r)^−360)] ≈ $1,257.50.
- Peter will pay 10% of his income = 0.10 × $2,985 = $298.50, so the rent must cover ≈ $1,257.50 − $298.50 ≈ $959.00.
- He planned $900, so he should raise it by about $59 → $60 (closest choice).