Question

Question 13 of 15 Trevor invested the profit of his business in an investment fund that was earning 2.25% compounded monthly. In 3 years, he began withdrawing $2,500 from this fund at the end of every 6 months. If the money in the fund lasted for the next 5 years, how much money did he initially invest in the fund? Round to the nearest cent

Answer 1

Computation of size of fund required in year 3 to facilitate 5 years of cash withdrawal:

Periodic rate = 0.0225/12 = 0.001875 p.m.

Periods	Cash Flow (C)	PV Factor Computation	PV Factor (F)	PV (=C x F)
1	$2,500	1/ (1+0.001875)6	0.988823460535867	$2,472.058651
2	$2,500	1/ (1+0.001875)12	0.977771836106127	$2,444.429590
3	$2,500	1/ (1+0.001875)18	0.966843730592969	$2,417.109326
4	$2,500	1/ (1+0.001875)24	0.956037763482347	$2,390.094409
5	$2,500	1/ (1+0.001875)30	0.945352569689585	$2,363.381424
6	$2,500	1/ (1+0.001875)36	0.934786799386930	$2,336.966998
7	$2,500	1/ (1+0.001875)42	0.924339117833031	$2,310.847795
8	$2,500	1/ (1+0.001875)48	0.914008205204328	$2,285.020513
9	$2,500	1/ (1+0.001875)54	0.903792756428320	$2,259.481891
10	$2,500	1/ (1+0.001875)60	0.893691481018701	$2,234.228703
			Total PV	$23,513.619301

Fund size should be of $ 23,513.62 on year 3^rd.

Initial investment or value of this fund in year 0 can be computed as:

PV = FV/(1+r) ⁿ

FV = $ 23,513.62

r = 0.001875

n = 3 years x 12 months = 36 periods

PV = $ 23,513.62/ (1+0.001875)³⁶

       = $ 23,513.62/ (1.001875)³⁶

       = $ 23,513.62/ 1.06976264604489

       = $ 21,980.2215818005 or $ 21,980.22

Trevor initially invested $ 21,980.22 in the fund.