Question

Marin Inc. wishes to accumulate $1,430,000 by December 31, 2030, to retire bonds outstanding. The company deposits $220,000 on December 31, 2020, which will earn interest at 10% compounded quarterly, to help in the retirement of this debt. In addition, the company wants to know how much should be deposited at the end of each quarter for 10 years to ensure that $1,430,000 is available at the end of 2030. (The quarterly deposits will also earn at a rate of 10%, compounded quarterly.)

Annuity of value of quarterly deposits: __________

Answer 1

Step 1 :	Future value of $220000
	FV= PV*(1+r)^n
	Where,
	FV= Future Value
	PV = Present Value
	r = Interest rate =10%/4 =2.5%
	n= periods in number =10*4 =40
	= $220000*( 1+0.025)^40
	=220000*2.68506
	= $590714.04
Step 2 :	Calculation of amount to be deposited quarterly
	Amount needed = $1430000-590714.04
	=$839285.96
	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
	839285.96= C[ (1+0.025)^40 -1] /0.025
	839285.96= C[ (1.025)^40 -1] /0.025
	839285.96= C[ (2.6851 -1] /0.025]
	C=$12451.84
	Quarterly deposit = $12451.84