Question

A small company wishes to set up a fund that can be used for technology purchases over the next 6 years. Their forecast is for $22,000 to be needed at the end of year 1, decreasing by $2,000 each year thereafter. The fund earns 9% per year. How much money must be deposited to the fund at the end of year 0 to just deplete the fund after the last withdrawal? $

Answer 1

Fund needed in years-

year 1= 22000$

year 2=20000$

year 3= 18000$

Year 4= 16000$

year 5=14000$

year 6= 12000$

so total amount we need to withdraw in total 6 years = $102000

but we will earn an interest of 9% each year

which means we need amount less than 102000

we will try to find the value with compounding formula if we invest $80000

total interest amount in year 1= 9% of 80000 i.e 7200

so we have a total of 87200 and we withdraw 22000 and remaining amount is 87200-22000=65200

then next year we will earn interest on 65200 i.e 9% and the process goes on

using excel we can find the exact value

	amount deposited	interest earned	total amount after interest	amount withdrawn	balance
0	78506
1		7065.54	85571.54	22000	63571.54
2		5721.4386	69292.9786	20000	49292.98
3		4436.368074	53729.34667	18000	35729.35
4		3215.641201	38944.98787	16000	22944.99
5		2065.048909	25010.03678	14000	11010.04
6		990.9033105	12000.94009	12000	0.940094

we need to deposit $78506 in year 0