Question

A deposit of X is made at the end of the year for ten years in order to accumulate a fund which will make payments of 100 at end of year forever, where the payments will start at the end of year 11. Find x if the effective interest rate is 6%. Show all work and equations.

Answer 1

Step 1	Value of perpetuity at the end of 10 year
	=$100/0.06
	=1666.66667
Step 2	We can calculate X by using following formula
	Future Value of an Ordinary Annuity
	c= Cash Flow	X
	i= Interest Rate	0.06
	n= Number Of Periods	10
	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	1666.67= X[ (1+0.06)^10 -1] /0.06
	1666.67= X[ (1.06)^10 -1] /0.06
	1666.67= X[ (1.7908 -1] /0.06]
	X =126.45