Question

Fund X earns 5% effective annual interest, while Fund Y earns 7% effective annual interest (and both start off with no money in them). You invest $500 into fund X at the end of each year for 20 years and at the end of each year, withdraw the year’s interest and deposit it into Fund Y . Find the accumulated value in Fund Y at the end of the 20 years. please dont use excel to solve

Answer 1

solution

fund X earns = 5%

fund Y earns = 7%

here i invest $500 into X at te end of each year for 20 years

and withdraw interest from X and invest it in Y

so to find the accumilated value in fund Y at te end of 20 years. we need to find the interest from X that is the deposit of Y

so to find fund X interest(that is fund Y deposit)

YEARS	DEPOSIT(END OF THE YEAR)	TOTAL	INTEREST(5%)
1	500	500	--------
2	500	500+500=1000	25
3	500	500+1000=1500	50
4	500	500+1500=2000	75
5	500	500+2000=2500	100
6	500	500+2500=3000	125
7	500	500+3000=3500	150
8	500	500+3500=4000	175
9	500	500+4000=4500	200
10	500	500+4500=5000	225
11	500	500+5000=5500	250
12	500	500+5500=6000	275
13	500	500+6000=6500	300
14	500	500+6500=7000	325
15	500	500+7000=7500	350
16	500	500+7500=8000	375
17	500	500+8000=8500	400
18	500	500+8500=9000	425
19	500	500+9000=9500	450
20	500	500+9500=10000	475

now we have interest of fund X for 20 years that is deposited in fund Y at the end of each year

next we can find the accumilated value in Y at the of 20th year

so

fund Y

YEARS	DEPOSIT(END OF THE YEAR	TOAL	INTEREST (7%)
1	-------------	--------------	------------
2	25	25	--------------
3	50	50+25=75	1.75
4	75	75+75=150	5.25
5	100	100+150=250	10.5
6	125	125+250=375	17.5
7	150	150+375=525	26.25
8	175	175+525=700	36.75
9	200	200+700=900	49
10	225	225+900=1125	63
11	250	250+1125=1375	78.75
12	275	275+1375=1650	96.25
13	300	300+1650=1950	115.5
14	325	325+1950=2275	136.5
15	350	350+2275=2625	159.25
16	375	375+2625=3000	183.75
17	400	400+3000=3400	210
18	425	425+3400=3825	238
19	450	450+3825=4275	267.7
20	475	475(NOT IN THIS YEAR)+4275=4750	299.25
TOTAL			1994.95

so we get the answer the accumilated amount at the 20th year is = 1994.95

note: the amount is deposited at the end of every year so interest will credit in the last of next year and we get interest for the amount that deposited previous years also