ANNUITIES & SINKING FUNDS 8
Annuities & Sinking Funds
Introduction
When it comes to business investing and expansion, two tools in the toolbox that are often used include sinking funds and annuities. These tools may be a little hard to understand for the layperson. However, with a little consideration and review, the picture can be quite clear. The scenario posed for this assignment is fairly basic. There is a business that owns a vinyl fencing company. There are two purchases that are on the horizon. One is an annuity as is being offered by an insurance company. Regardless of the option chosen, the stated need in terms of savings is $2600 every six months. There is a choice of an ordinary annuity and an annuity due. The second matter centers on the need to purchase a machine. The machine costs $23,000 and it needs to be purchased within the next three years as that is when the existing machine will reach the end of its useful life. The idea is to use a sinking fund that compounds quarterly and that earns an annual rate of 7.2 percent. While one must be careful and diligent in making the necessary calculations, the choices to be made in the above scenarios are quite clear.
Purchase One - Annuity Decision
Ordinary Annuity
The scenario for the annuity makes is clear that the desired payment per six months is $2600. However, since the annuities in question...
The ordinary formula and variables would be as follows:
(UTEP, 2018).
· As can be seen by the contextual paragraph noted above, PMT would be $2600 because that is the desired payment per compounding period. Similarly, if a zero balance is acceptable at the end, then that means PV is what needs to be in the annuity right now.
· Also noted in the paragraph is what “i” would be. It would be r/m, where r is the annual rate and m is the amount of times compounded per year. Since the compounding is semi-annual, m would be 2. The rate, as given in the problem, is five percent, or 0.05. In other words, r/m would become 0.05 / 2, which is 0.025. Since i has already been calculated, most of the bottom is taken care of.
· Based on the above, we can figure out what -n would be. Over five years, there would be 10 periods of compounding (5 years * 2 times per year). Thus, -n would be -10. Given that, the bottom would become 1 – (1 + 0.025) -10. Parentheses and exponents have to be cleared first, in that order. Thus, one would first simplify that to 1 – (1.025) -10. 1.025 to the negative tenth power would be 0.7812, rounded to the fourth digit. This leaves 1 – 0.7812, or 0.2188. This leaves…
· 2600 = PV (0.025/0.2188)
· 2600 = PV (0.1143)…
