Question

You are thinking about renting out your condo rather than selling it. You can get $200,000 if you sell your condo to an eager buyer today, but only $100,000 if you wait to sell it. You expect to earn $5,000 per month (including all expenses) at a discount rate of 12%. What is the minimum number of months you need to rent it out for this to be an acceptable investment?

Answer 1

Minimum no of installments will be required in such manner that PV will be 200,000
Assumed there are N monthly installments
Monthly Interst rate= 1%
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Present value	=5000*(((1-(1 + 1%) ^-N)) / 1%)
Present value	=5,00,000*(((1-(1.01) ^-N))
Present value	=5,00,000-500000*(1.01) ^-N))
PV of sale price	=100000/(1+1%)^N
Total should be atleast 200000
200000	=5,00,000-500000*(1.01) ^-N)) + 100000/(1.01)^N
-300000	=-500000*(1.01) ^-N)) + 100000/(1.01)^N
-300000	=-400000/(1.01)^N
300000	=400000/(1.01)^N
(1.01)^N	=400000/300000
(1.01)^N	1.333333333
N Log 1.01=	Log 1.333
N Log 1.01=	Log 1.333
N *0.00432137=	0.12493874
N	=0.12493874/0.00432137
N =	29
So minimum 29 installment should be there to make sure that there is no loss