Question

1.
a. Steve Hitchcock is 43 years old today and he wishes to accumulate $469,000 by his 67th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 43th through his 66th birthdays. What annual deposit must Steve make if the fund will earn 12% interest compounded annually?
b. Cindy Ross has $20,200 to invest today at 12% to pay a debt of $62,738. How many years will it take her to accumulate enough to liquidate the debt?

Answer 1

• All working forms part of the answer
• Working for Answer 1

Answer may vary slightly due to rounding off

Total years from 43^rd birthday to 66^th birthday = 24

PV for 25^th year at 12% = [(1/(1.12)²⁵] = 0.05882

PV of $469000 at 25^th year = $469,000 x 0.05882 = $27,588.13

PV Annuity Factor for 24 years at 12% = 7.784315

                Amount to be deposited each year will be 27588.13/7.784315 = $3544

                Verification:

               

Years	Opening Balances + $3544 deposit each year	Interest @ 12%	Closing Balance (including Interest)
1	3544	425	3969
2	7513	902	8415
3	11959	1435	13394
4	16938	2033	18971
5	22515	2702	25217
6	28761	3451	32212
7	35756	4291	40047
8	43591	5231	48822
9	52366	6284	58650
10	62194	7463	69657
11	73201	8784	81985
12	85529	10264	95793
13	99337	11920	111257
14	114802	13776	128578
15	132122	15855	147976
16	151520	18182	169703
17	173247	20790	194037
18	197581	23710	221290
19	224834	26980	251815
20	255359	30643	286002
21	289546	34745	324291
22	327835	39340	367176
23	370720	44486	415206
24	418750	50250	$469000

Hence, proved that at the end of 24^th year, amount matured will be $469,000

• Answer 2

Year	Opening Investment balance (A)	Interest earned at 12% (B = A x 12%)	Ending Investment balance (C=A+B)
1	20200	2424	22624
2	22624	2715	25339
3	25339	3041	28380
4	28380	3406	31785
5	31785	3814	35599
6	35599	4272	39871
7	39871	4785	44656
8	44656	5359	50014
9	50014	6002	56016
10	56016	6722	$62,738

Hence, at the end if 10 year, the investment will yield $62,738 at an interest rate of 12%