PLEASE READ: Please solve the problem without the use of Excel and its formulas.

Question

PLEASE READ:

Please solve the problem without the use of Excel and its formulas. I am more of a visual learner so a cash flow drawn out or something similar would be extremely helpful :) Thank you!

(6) Alex is considering buying a house. He is planning to rent the house and sell it after few years to buy a bigger house. His current plan is to sell the house after 5 years. The house worth $255,000 today. He can get $255,000 mortgage for 9% nominal annual interest rate, compounded monthly. Based on the information he collected, the house can be sold for 385,000 in 5 years. The monthly maintenance fee is $200. How much should he charge the tenants (monthly) in rent to cover the maintenance fee and the mortgage? Excel solution is NOT accepted.

Explanation / Answer

Consider the given problem here the nominal annual interest rate is “9%” compounded monthly, => the monthly nominal interest rate is “9/12 = 0.75%”. Now, let’s assume that “$X” be the monthly rent and “$200” be the monthly maintenance cost, => net cash inflow is “X-200”, and in “5 year” there are 60 months. So, the following relation should hold good.

=> 255,000*(1+0.75%)^60 = [(x-200)/i]*[(1+i)^n-1], here “i=0.75%” and “n=60”.

=> 255,000*(1.0075)^60 = [(x-200)/0.0075]*[(1.0075)^60-1],   

=> 255,000*(1.565681) = [(x-200)/0.0075]*(0.565681),   

=> 399,248.6619 = [(x-200)/0.0075]*(0.565681),    

=> 399,248.6619/0.565681 = [(x-200)/0.0075],

=> 705,784.1113*0.0075 = (x-200), => 5,293.38 = (x-200), => 5,293.38 + 200 = x,

=> $x = $5,493.38 = $5,493.

So, the person should charge “$X=$5,493” per month in order to meet the entire mortgage.

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