Question

3.2     You put $1000 in a savings account at 10% annually compounded interest.                                                                                                                                      

a. How much could you take out each year and still keep the original $1000 in the account? Complete the table below to support your conclusion.

Year	Beginning balance	Interest earned (10%)	Withdrawal	Ending balance
1	$1000			$1000
2	1000			1000
3	1000			1000
4	1000			1000

b. If you left half of the interest earnings in the account, at what rate would the balance grow from year to year? Complete the table to show your calculations.

Year	Beginning balance	Interest earned (10%)	Withdrawal (50% of interest)	Ending balance
1	1000
2
3
4
			Annual growth rate =	%

c. If you took out 80% of the interest earnings in the account, at what rate would the balance grow each year? Complete the table to show calculations.

Year	Beginning balance	Interest earned (10%)	Withdrawal (80% of interest)	Ending balance
1	1000
2
3
4
			Annual growth rate =	%

Answer 1

	a		A	B=A*10%	C=B	D=A+B-C
		Year	Beginning balance	Interest earned (10%)	Withdrawal	Ending balance
		1	$1,000	$100	$100	$1,000
		2	$1,000	$100	$100	$1,000
		3	$1,000	$100	$100	$1,000
		4	$1,000	$100	$100	$1,000
	b
			A	B=A*10%	C=50%*B	D=A+B-C
		Year	Beginning balance	Interest earned (10%)	Withdrawal	Ending balance
					(50% of interest)
		1	$1,000.00	$100.00	$50.00	$1,050.00
		2	$1,050.00	$105.00	$52.50	$1,102.50
		3	$1,102.50	$110.25	$55.13	$1,157.63
		4	$1,157.63	$115.76	$57.88	$1,215.51
					Annual growth rate =	5%
			Annual Growth Rate =		0.05	((1215.51/1000)^(1/4))-1
			Annual Growth Rate =		5.0%
	c
			A	B=A*10%	C=80%*B	D=A+B-C
		Year	Beginning balance	Interest earned (10%)	Withdrawal	Ending balance
					(80% of interest)
		1	$1,000.00	$100.00	$80.00	$1,020.00
		2	$1,020.00	$102.00	$81.60	$1,040.40
		3	$1,040.40	$104.04	$83.23	$1,061.21
		4	$1,061.21	$106.12	$84.90	$1,082.43
					Annual growth rate =	2%
			Annual Growth Rate =		0.02	((1082.43/1000)^(1/4))-1
			Annual Growth Rate =		2.0%