Question

You rent out an apartment for 15 years, with rent starting at $500 per month and increasing 3% each year. Immediately after receiving rent payments you deposit the rent payment into an account with i(12) = .06. If there are no other deposits or withdrawals into this account then how much is in the account after the 15 year period?

Answer 1

Year 1

The beginning rent of the apartment was $500

The APR rate was given to be 6% yearly or 6/12 = 0.5% montlhy

Usinf FV of annuity payments we have year end balance of

FV annuity = PMT [(1+r)^n -1) /r ] = 500 [(1+0.005)^12 - 1 / 0.005

Year 1 ending balance = $6167.78

Year 2

The rent grows at a rate of 3% pa

so second year rent is 500*(1.03) = 515.0

FV annuity + FV of year 1 balace = 515 [(1+0.005)^12 - 1 / 0.005 + 6167.78(1+0.005)^12

= $12901.01

Year 3

The rent grows at a rate of 3% pa

so second year rent is 515*(1.03) = 530.45

FV annuity + FV of year 1 balace = 530.45 [(1+0.005)^12 - 1 / 0.005 + 12901.01(1+0.005)^12

= $20240.12

Year 4

The rent grows at a rate of 3% pa

so second year rent is 530.45*(1.03) = 546.36

FV annuity + FV of year 1 balace = 546.36 [(1+0.005)^12 - 1 / 0.005 + 20240.12(1+0.005)^12

= $28,228.18

and for upto 15 yeras we get the following table of balance

Rate	6%		Year Ending Balance
Year	Rent
1	500.00	$6,167.78	$6,167.78
2	515.00	$6,352.81	$12,901.01
3	530.45	$6,543.40	$20,240.12
4	546.36	$6,739.70	$28,228.18
5	562.75	$6,941.89	$36,911.13
6	579.64	$7,150.15	$46,337.87
7	597.03	$7,364.65	$56,560.55
8	614.94	$7,585.59	$67,634.67
9	633.39	$7,813.16	$79,619.39
10	652.39	$8,047.56	$92,577.69
11	671.96	$8,288.98	$1,06,576.67
12	692.12	$8,537.65	$1,21,687.73
13	712.88	$8,793.78	$1,37,986.95
14	734.27	$9,057.59	$1,55,555.28
15	756.29	$9,329.32	$1,74,478.91