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?

Peter should a minimum of $960 for the rent of the other half of the duplex in order to complete payment of mortgage of the house in 30 years.

How much rent should Peter charge?

The amount rent Peter should charge will be calculated as follows:

After 10% down payment, amount Peter will pay is 90% of his purchase price:

90% of purchase price = 226,950*0.9 = $204255

Assuming the mortgage is compounded monthly, the total monthly mortgage payment is determined from the amortization formula as follows:

A=P(i(1+i)^n)/((1+i)^n-1)

where

A = monthly payment
P = amount borrowed (present value) = $204255
i = monthly interest = 0.0625/12
n = number of months = 30*12 = 360

Calculating the monthly paymen:

A = 204255(.0625/12 (1+.0625/12)^360)/((1+.0625)^360-1)

A = $1257.63

His monthly payment is 10% of his income

Monthly payment = 10% of $2985 = $298.50

Therefore, the minimum rent = 1257.63 - $298.50

minimum rent = $959.13

Therefore, Peter should charge a minimum of $960 for the rent of the other half of the duplex.

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