Question

Lori wants to give her daughter $25,000 in 8 years to start her own business. Lori has already saved $5,000 already for this purpose. How much should Lori invest annually, at the beginning of each year, at an annual interest rate of 7%, compounded annually, to have $25,000 in 8 years?

Answer 1

Step 1 :	Future value of $5000
	FV= PV*(1+r)^n
	Where,
	FV= Future Value
	PV = Present Value
	r = Interest rate
	n= periods in number
	= $5000*( 1+0.07)^8
	=5000*1.71819
	= $8590.93
Step 2 :	Amount remaining to be have from annuity
	=$25000-8590.93
	=$16409.07
Step 3:	Future Value of an Annuity Due
	= C*[(1+i)^n-1]/i] * (1+i)
	Where,
	c= Cash Flow per period
	i = interest rate per period
	n=number of period
	16409.07= C[ (1+0.07)^8 -1 /0.07] * (1 +0.07)
	16409.07= C[ (1.07)^8 -1 /0.07] * 1.07
	16409.07= C[ (1.7182 -1 /0.07] * 1.07
	C =1494.72
	Annual payment = $ 1994.72