Question

A person deposits $60 at the end of each month in an account which earns 12.5% compounded monthly for 17 years. The person then stops making the deposits, but allows the money to remain in the bank earning the same interest for 5 more years. a. Find the value of this account at the end of 22 years. $ b. State the total amount of interest earned on this account. $

Answer 1

a)	Step 1 :Value of annuity at the end of year 17
	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i
	Where,
	C= Cash Flow per period
	i = interest rate per period =12.5%/12 =1.041666667%
	n=number of period =17*12 =204
	= $60[ (1+0.01041666667)^204 -1] /0.01041666667
	= $60[ (1.01041666667)^204 -1] /0.01041666667
	= $60[ (8.2814 -1] /0.01041666667]
	= $41,940.70
	step 2 :Value of $41940.70 at the end of year 22 from now
	FV= PV*(1+r)^n
	Where,
	FV= Future Value
	PV = Present Value
	r = Interest rate
	n= periods in number
	= $41940.7*( 1+0.01041667)^60
	=41940.7*1.86222
	= $78102.65
b)	Total payment made = $60*12*17
	=$12240
	Total interest earned = $78102.65-12240
	$ 65,862.65