Question

Peter got a 8-year assignment in Argentina. Consequently, he will rent out his three-bedroom house in Hancock to an old friend, and given their friendship, Peter only requires end of the year payments (thus no monthly pmts) to be deposited in a savings account created solely for this purpose. Rental income will be 18774 dollars per year but maintenance/repair costs will be 758 dollars in the first year and thereafter increase by 289 dollars per year. The tenant will be doing the maintenance/repair operations and therefore, at the end of each year, deposits the annual rent amount net of maintenance costs. Compute how much money will Peter have in his savings account upon his return (8 years from now) given that the proxy interest rate is 6% per year, compounded annually. (note: round your answer to the nearest cent, and do not include spaces, currency signs, plus or minus signs, or commas)

Answer 1

Rental income every year = 18774

Maintenance/Repair cost = 758 in first year and increasing 289 per year

deposit is rental income - repair cost per year

i=0.06

T = 8yrs

Using formula FV = P *(1+i)^n for calculating future worth of any given payment

using excel

i				0.0600
Year	Rental Income	Repair Cost	Deposit	future worth factor	future worth
1	18774	758	18016	1.5036	27,089.40
2	18774	1047	17727	1.4185	25,146.09
3	18774	1336	17438	1.3382	23,335.98
4	18774	1625	17149	1.2625	21,650.22
5	18774	1914	16860	1.1910	20,080.53
6	18774	2203	16571	1.1236	18,619.18
7	18774	2492	16282	1.0600	17,258.92
8	18774	2781	15993	1.0000	15,993.00
					1,69,173.31

showing formula in excel

i				0.06
Year	Rental Income	Repair Cost	Deposit	future worth factor	future worth
1	18774	758	=B3-C3	=(1+$E$1)^(8-A3)	=D3*E3
2	18774	=C3+289	=B4-C4	=(1+$E$1)^(8-A4)	=D4*E4
3	18774	=C4+289	=B5-C5	=(1+$E$1)^(8-A5)	=D5*E5
4	18774	=C5+289	=B6-C6	=(1+$E$1)^(8-A6)	=D6*E6
5	18774	=C6+289	=B7-C7	=(1+$E$1)^(8-A7)	=D7*E7
6	18774	=C7+289	=B8-C8	=(1+$E$1)^(8-A8)	=D8*E8
7	18774	=C8+289	=B9-C9	=(1+$E$1)^(8-A9)	=D9*E9
8	18774	=C9+289	=B10-C10	=(1+$E$1)^(8-A10)	=D10*E10
					=SUM(F3:F10)