Question

Three years after 25 years of saving. Lucy withdrew $9,500 each year for a period of 4 years. In the fifth, sixth, and seventh years, she only withdrew $7,000 per year. In the eighth year, she decided to withdraw the remaining money in her account. If Lucy has saved $1,300 each year with an interest rate of 5% per year compounded monthly throughout the whole period, what was the amount she withdrew at the end of the eighth year? Draw a cash flow diagram for the given transactions and show all of your calculations.

Answer 1

Rate of Interest	5%	per Annum
Compounding rate	Monthly
Formula
A = Final Amount
P = Principal Amount
r = Rate of interest in decimal
n = No of times it is compounded
t =Number of Years
Year	Deposit Amount	No of years remaining (t) =25 years of saving +3 years waiting	Number of Times it is Compounded in a year (n)	Final Amount (A)
1	1300	28	12	5,256.45
2	1300	27	12	5,000.61
3	1300	26	12	4,757.22
4	1300	25	12	4,525.68
5	1300	24	12	4,305.40
6	1300	23	12	4,095.85
7	1300	22	12	3,896.50
8	1300	21	12	3,706.85
9	1300	20	12	3,526.43
10	1300	19	12	3,354.79
11	1300	18	12	3,191.51
12	1300	17	12	3,036.17
13	1300	16	12	2,888.40
14	1300	15	12	2,747.82
15	1300	14	12	2,614.07
16	1300	13	12	2,486.84
17	1300	12	12	2,365.80
18	1300	11	12	2,250.66
19	1300	10	12	2,141.11
20	1300	9	12	2,036.90
21	1300	8	12	1,937.76
22	1300	7	12	1,843.45
23	1300	6	12	1,753.72
24	1300	5	12	1,668.37
25	1300	4	12	1,587.16
Value at the end of 28 years				76,975.54
Year	The value available at year	Amount is withdrawn	Remaining Amount	The value available at the end of the year after withdrawal adding interest compounded for the year
1	76,975.54	-9500	67,475.54	70,927.72	67475.54*POWER((1+0.05/12),12)
2	70,927.72	-9500	61,427.72	64,570.48
3	64,570.48	-9500	55,070.48	57,887.99
4	57,887.99	-9500	48,387.99	50,863.61
5	50,863.61	-7000	43,863.61	46,107.75
6	46,107.75	-7000	39,107.75	41,108.58
7	41,108.58	-7000	34,108.58	35,853.64
	Amount Available for withdrawal at the end		35,853.64