Question

You have 2000 invested in a bank X earning 5% effective annual interest. At the end of each year, you withdrawl that year’s interest in addition to 100 from bank X and deposit both in bank Y, which earns 6% effective annual interest. How much is in bank Y at the end of the 20 years?

Answer 1

Account X steps:

1. Begning of year balance: Start with 2,000 for year 1 then take End of the year balance of previous year for subsequent years

2. Interest Earned at 5% = Beginning of year balance *5%

3. Principal Withdrawn: remains constant as 100 for each year

4. End of year Balance: Begining of year balance - Principal withdrawal (100)

5. Total amount withdrawn at the year end = Interest earned + Principal withdrawn

Account Y steps:

1. Begning of year balance: Start with 0 for year 1 then take End of the year balance of previous year for subsequent years

2. Interest Earned at 6% = Beginning of year balance *6%

3. Amount deposited at the end of the year = Total amount withdrawn at the year end from Account X. This item number 5 above

4. End of the year balance = Begining of the year balance + Interest earned at 6% + Amount deposited at the end of the year

5. Answer is 5958.3 i.e. the last number in the last column

	Account X Details:					Account Y details:
Year	Begning of year balance	Interest Earned at 5% (which will be withdrawn)	Principal Withdrawn	End of year Balance	Total amount withdrawn at the year end		Beginning of year balance	Interest Earned at 6%	Amount deposited at the end of the year	End of year Balance
1	2000	100	100	1900	200		-	-	200.0	200.0
2	1900	95	100	1800	195		200.0	12.0	195.0	407.0
3	1800	90	100	1700	190		407.0	24.4	190.0	621.4
4	1700	85	100	1600	185		621.4	37.3	185.0	843.7
5	1600	80	100	1500	180		843.7	50.6	180.0	1,074.3
6	1500	75	100	1400	175		1,074.3	64.5	175.0	1,313.8
7	1400	70	100	1300	170		1,313.8	78.8	170.0	1,562.6
8	1300	65	100	1200	165		1,562.6	93.8	165.0	1,821.4
9	1200	60	100	1100	160		1,821.4	109.3	160.0	2,090.7
10	1100	55	100	1000	155		2,090.7	125.4	155.0	2,371.1
11	1000	50	100	900	150		2,371.1	142.3	150.0	2,663.4
12	900	45	100	800	145		2,663.4	159.8	145.0	2,968.2
13	800	40	100	700	140		2,968.2	178.1	140.0	3,286.2
14	700	35	100	600	135		3,286.2	197.2	135.0	3,618.4
15	600	30	100	500	130		3,618.4	217.1	130.0	3,965.5
16	500	25	100	400	125		3,965.5	237.9	125.0	4,328.5
17	400	20	100	300	120		4,328.5	259.7	120.0	4,708.2
18	300	15	100	200	115		4,708.2	282.5	115.0	5,105.7
19	200	10	100	100	110		5,105.7	306.3	110.0	5,522.0
20	100	5	100	0	105		5,522.0	331.3	105.0	5,958.3