Question

Catherine deposited $31,000 into a fund at the beginning of every quarter for 17 years. She then stopped making deposits into the fund and allowed the investment to grow for 4 more years. The fund was growing at 5.31% compounded monthly.

a. What was the accumulated value of the fund at the end of year 17?

b. What was the accumulated value of the fund at the end of year 21?

c. What is the total amount of interest earned over the 21-year period?

Answer 1

	First, we have to compute the effective annual interest rate and then quarterly interest rate
	Effective annual interest rate =		5.44%
	(1+5.31%/12)^12-1
	Interest rate compounded quarterly=	((1+5.44%)^(1/4)-1)*4
	Interest rate compounded quarterly=	5.33%
	Quarterly rate = 5.33%/4		1.33%
Ans a)	we have to use finanical calculator to solve this
	Put in calculator, set the calculator at BEGIN mode
	PV		0
	PMT		-31000
	I		1.33%
	N	17*4	68
	Compute FV		$3,397,504.95
	ans =		$3,397,504.95
Ans b)	Accumulated value at the end of 21th year
	Put in calculator
	PV		($3,397,504.95)
	PMT		0
	I		1.33%
	N	4*4	16
	Compute FV		$4,199,530.66
	ans =		$4,199,530.66
Ans c)
	Total amount of interest earned =	$ 2,091,530.66
	4199530.66-31000*17*4