Question

QUESTION 4

Jefta has a 30-year policy with SANLAM. The illustrated growth rate is 6% p.a. compounded monthly and the premium increases every January 01 by 10%. The initial premium was $300 per month. Jefta’s first monthly premium was deducted on January 31, 1998.

1. Determine the monthly premium in the last year.

2. Determine the maturity value. A compact disc press is purchased for $1.2 million and is expected to rise in cost at a rate of 8% p.a., whilst it will depreciate at a rate of 7.5% p.a. A sinking fund is set up to make provision for the replacement of the machine in ten years’ time, and pays interest at a rate of 9.25% p.a. compounded monthly.

3. Determine the monthly amount that has to be deposit into the sinking fund to realize enough money for a replacement machine in ten years’ time. Payments start immediately and end on the day that the replacement machine is purchased.

4. After five years new technology in Compact Discs are introduced to the market. This machine will cost $2 million. If you decide to replace your current machine immediately, how much money will you have to borrow to purchase the new equipment, if you use the sinking fund and the sales of the old machine towards paying for this new machine?

Answer 1

In these type of questions, it is always advised to create a table/financial model like I did (attached below).   

It is also to be noted that the answers are based on logical assumptions and might not match exactly to the book answer.

As per the data given by you:

1) Monthly premium in 2017 (last year) is $1835

2) At maturity value the fund will be $1.202 million.

3) The sinking fund set for the purchase of the disc will contribute approx $9350 per month and $112200 yearly.

4) If after 5 years a new tech disc is purchased worth $2 million, the borrowing will be around $329245.

Step by step approach mentioned below:

Year	Number	Monthly premium	Annual premium	Maturity value
1998	0	300	3600	3600
1999	1	330	3960	7782
2000	2	363	4356	12618
2001	3	399	4792	18188
2002	4	439	5271	24580
2003	5	483	5798	31894
2004	6	531	6378	40239
2005	7	585	7015	49736
2006	8	643	7717	60521
2007	9	707	8489	72742
2008	10	778	9337	86566
2009	11	856	10271	102177
2010	12	942	11298	119777
2011	13	1036	12428	139593
2012	14	1139	13671	161874
2013	15	1253	15038	186896
2014	16	1378	16542	214965
2015	17	1516	18196	246420
2016	18	1668	20016	281634
2017	19	1835	22017	321022	Disc press price	Depreciation	Sinking fund contribution
2018	20	2018	24219	365041	1200000	1200000	112200
2019	21	2220	26641	414197	1296000	1110000	235230
2020	22	2442	29305	469048	1399680	1026750	370135
2021	23	2686	32235	530214	1511654	949744	518062
2022	24	2955	35459	598375	1632587	878513	680268	New tech disc	Amt available
2023	25	3250	39005	674287	1763194	812624	858130	2000000	1670755
2024	26	3575	42905	758781	1904249	751678	1053160
2025	27	3933	47196	852777	2056589	695302	1267016
2026	28	4326	51916	957290	2221116	643154	1501514
2027	29	4759	57107	1073440	2398806	594918	1758646
2028	30	5235	62818	1202465	2590710	550299	2040598
					Sinking fund	2040411		Replace machine after 5 years	329245