Pre-Calculus Report: Comparing Stock and Bond Investment Growth

This assignment uses pre-calculus to analyze and compare the growth of stock and bond investments over a 40-year period, considering different inflation rates. It begins by differentiating between linear and exponential growth, then calculates the normal value of a stock portfolio and a bond investment using compound interest formulas. Maple plots are used to visualize the growth trajectories. The analysis extends to evaluating the impact of a 3% inflation rate on both investments and determining the annual inflation rate using the Consumer Price Index (CPI). The report concludes that stocks offer greater growth potential but require more research, while bonds offer less loss but slower growth. The study highlights the importance of understanding investment options and their sensitivity to inflation.

Running head: PRE-CALCULUS 1
Topic
Name of Student
Institution affiliation

PRE-CALCULUS 2
Introduction
The aim of this assignment to show the difference between Stock and bonds, that is
according to their growth and to show the better option when trying to invest. Different
inflation rates will be used for the two to compare the above information
1
To state the difference between the linear growth and exponential growth
The main difference between linear growth and exponential growth is that linear growth
expands at a constant rate while exponential growth expands at a zooming rate.
2
To calculate the normal value of the stock portfolio after 40 years.
We will apply the formula of compound interest to calculate this sum. Firs, to understand the
formula of compound interest i.e.
A = P (1 +
r
n )nt
Where A is the amount, P is the principle, r is the rate, n is the number of times interest is
compounded per year. The formula for obtaining the number of stocks is given by:
As = 25000(1 + 0.07) t
=25000 (1.07)40
= 25000 (14.974457839)
= 374361.45
3

PRE-CALCULUS 3
To calculate the normal value of bond after 40 years.
The formula of obtaining the amount of bond is given by
Ab = 25000 (1 + 0.0155) t
Where t is the time in years. By inserting the value of t (40) in the formula we will obtain:
Ab = 25000 (1 + 0.0155) t
= 25000 (1.0155) 40
= 25000 (1.8501812)
= 46252.70
4
Drawing a maple plot
0 5 10 15 20 25 30 35 40 45
0
5000
10000
15000
20000
25000
30000 25000(1 + 0.07) t
25000(1 + 0.0155)t
5
a) To determine the amount of Stock provided a 3 % inflation rate after 40 years. The
formula for obtaining Amount of stock adjusts to

PRE-CALCULUS 4
As = 25000(1 + (0.07 – 0.03)) t
= 25000 (1.04) t
= 25000 (1.04)40
= 25000 (4.8010206279)
= 120025.50
b) To determine the amount of bond after 40 years provided a 3 % inflation rate.
We use the formula given i.e.
Ab = 25000 (1 + (0.0155-0.03)) t
= 25000 (0.9855)40
= 25000 (0.557526)
= 13938
c) Drawing a maple plot for the adjusted 3 % interests
0 5 10 15 20 25 30 35 40 45
0
5000
10000
15000
20000
25000
30000
25000 (1 + (0.0155-0.03)) t
25000 (1 + (0.0155-0.03)) t
The answer to question 6

PRE-CALCULUS 5
To obtain the annual inflation rate, we use the 12 – months Consumer Price Index (CPI).
We use the CPI for October 2017 and the CPI for October 2018.
The formula for obtaining inflation is: (Wasik, 2016)
% inflation = (CPI of 2018 – CPI of 2017)/ CPI of 2017 * 100%
The inflation rate of US in October is 2.5 %
We will use this information to obtain The amount of Stock after 40 years:
As = 25000(1 + (0.07-0.025)) t
= 25000 (1.045)40
= 25000 (5.8163645)
= 145409
a) To obtain the amount of bond in 40 years, we use the following formula:
Ab = 25000 (1 + (0.0155-0.025)) t
= 25000 (0.9905)40
= 25000 (0.682620)
=17065.50
c) The maple plot for this inflation rate:

PRE-CALCULUS 6
0 5 10 15 20 25 30 35 40 45
0
5000
10000
15000
20000
25000
30000
Stock
Bond
Conclusion
From the graphs one can conclude that the major of investing in Stock is that you have a
chance to grow your money. One can notice that the amount grows gradually and therefore,
one is able to grow his money. It’s also the best way to stay ahead of inflation. One of the
disadvantages is that it requires a lot of time since you have to research companies to
determine the profit they make. The major advantage of investing in bonds is that it suffers
less loss. Comparing it with Stock, it grows slowly.

PRE-CALCULUS 7
Reference
.
BIBLIOGRAPHY Wasik, John E. (2016, August 17). Trading Stocks for Bonds Poses Its
Own Risk. The New
York Times, p.B4.