Question

The good news is that SAVING uses the same geometric series formula as BORROWING money! Assume you deposit $10 per month into a savings account with an annual interest rate of 30%, compounded monthly (a) Sketch the graph representing the amount that you've DEPOSITED into the account after r years. Hint: you can determine this formula and graph the function easily.) (b) In another color, copy your graph of f (r) from the previous slide. This is the total amount in your savings account after x years. (c) What do you notice about the two graphs? In full sentences below, describe the shapes of the graphs and how they determine the amount you've earned in interest changes over time.

Answer 1

		Cumulative amount DEPOSITED in x years=10*12*x	120*x
		Monthly interest rate=30/12=2.5%=0.025
		Compound Amount Factor=CAF=(F/A,i,N)=(((1+i)^N)-1)/i
		i=interest rate per period, N=Number of periods
		For one year deposit, N=12,(number of months)
		i=2.5%=0.0259(Monthly interest)
		CAF=(F/A, 2.5%,12)=((1.025^12)-1)/0.025=	13.79555
		Amount at end of year for monthly deposit=10*CAF=	$137.96		$459.85
		Annual Interest =30% =0.3
		CAF for x years of deposit =(F/A, 30%,x)=((1.3^x)-1)/0.3
		Total amount in savings account =137.96*CAF=459.85*((1.3^x)-1)
	C	NOTE: Amount deposited increases linearly with years
		Total amount in savings account increases exponentially because of compounding of interest
			x	A=120*x	B=459.85*((1.3^x)-1)
			Year	Cumulative amount Deposited	Total amount in savings account
			1	$120	$137.96
			2	$240	$317.30
			3	$360	$550.44
			4	$480	$853.53
			5	$600	$1,247.54
			6	$720	$1,759.76
			7	$840	$2,425.64
			9	$1,080	$4,416.63
			10	$1,200	$5,879.57
			11	$1,320	$7,781.40
			12	$1,440	$10,253.77
			13	$1,560	$13,467.86
			14	$1,680	$17,646.18
			15	$1,800	$23,077.98
						Cumulative amount Deposited $2,000 $1,800 $1,600 $1,400 $1,200 $1,000 Cumulative amount Deposited $800 $600 $400 $200 $0 0 10 12 14 16 $25,000 $20,000 $15,000 -cumulative amount Deposited 10,000 Total amount in savings account $5,000 $o 10 12 14 16