Question

2. Ronald Zoller is planning to retire at the end of the current year. He estimates that he will need $18,000 a year for the next 15 years to meet his needs. Assuming the appropriate interest rate is $8%, how much should Zoller deposit on December 31 of the current year in order to be able to withdraw $18,000 at the end of each of the next 15 years.

Table I used to solve this problem

Table factor I used to solve this problem

Final answer

Answer 1

rate of interest = 8%

at the end of 15 years Ronald Zoller requirement will be 0 means at the end of 15 the year closing balance = 0

so at last year(15 the year ) opening balance = 18000/1.08 = 16666.67

14th year closing balance = 15th year opening balance

14th year opening balance = (18000+16666.67)/1.08 = 32098.77

13th year closing balance = 14th year opening balance

13the year opening balance = (32098.77+18000)/1.08

= 46387.75

like this we can calculate the beginning amount of year 1.

Determination of year 1 opening amount in below table -

year	opening	interest	withdrawl	closing
1	154070.6	12325.65	18000	148396.3
2	148396.3	11871.7	18000	142268
3	142268	11381.44	18000	135649.4
4	135649.4	10851.95	18000	128501.4
5	128501.4	10280.11	18000	120781.5
6	120781.5	9662.517	18000	112444
7	112444	8995.519	18000	103439.5
8	103439.5	8275.16	18000	93714.66
9	93714.66	7497.173	18000	83211.83
10	83211.83	6656.947	18000	71868.78
11	71868.78	5749.502	18000	59618.28
12	59618.28	4769.463	18000	46387.75
13	46387.75	3711.02	18000	32098.77
14	32098.77	2567.901	18000	16666.67
15	16666.67	1333.333	18000	0

So Zoller should deposit on 31st dec. of the current year = $ 154070.6.

Please check with your answer and let me know.