Question

Question 3 When interest is compounded continuously, the following equation repre- sents the growth of your savings: P Poe" In this equation, P = current balance Po initial balance r growth constant, expressed as a decimal fraction t time invested. Determine the amount in your account at the end of each year if you invest $1000 at 8% (0.08) for 30 years. (Make a table.) Create a figure with four subplots. Plot time on the eaxis and current balance Pon the yaxis (a) In the first quadrant, plot versus Pin a rectangular coordinate system. (b) In the second quadrant, plot Iversus P scaling the waxis logarithmically. (c) In the third quadrant, plot Iversus P scaling the yaxis logarithmically (d) In the fourth quadrant, plot f versus P scaling both axes logarithmically. Which of the four plotting techniques do you think displays the data best?

Answer 1

P₀ = $1000

r = 0.08

e=2.72 (rounded to nearest 2 decimals places)

For ease of calculation, let us break down the formula

0.08t P PePo(e)1000 x (e0u1000 x 1.0832'

t (in years)	P ($)
1	1083.28
2	1173.32
3	1270.94
4	1376.68
5	1491.22
6	1615.29
7	1749.68
8	1895.26
9	2052.94
10	2223.75
11	2408.76
12	2609.17
13	2826.26
14	3061.40
15	3316.11
16	3592.01
17	3890.87
18	4214.59
19	4565.24
20	4945.07
21	5356.50
22	5802.16
23	6284.90
24	6807.81
25	7374.22
26	7987.75
27	8652.34
28	9372.21
29	10151.98
30	10996.62

Ofcourse, the more decimal places you consider for the value of e, more accurate results you would get.

The graphs

a)

2 14 Ti 8 6 4 5050505050505050505050505 CICI ㅣ 1 0 0 9 9 8 8 7 7 6 6 5 5 4 4 3 3 1 CI-- ($) umoury
b)
Current Balance 12500 12000 11500 11000 10500 10000 9500 9000 8500 8000 7500 7000 6500 6000 5500 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 01 02 0305 06 0.7 08 0.9 1 12 3 14 1.5 Tme dog base 10)
c)
o Current Balance 4.6 4.4 4.2 3.8 3.6 3.4 3.2 6 2.8 2.6 2.4 1.4 0.8 0.6 0.4 0.2 4 6 8 10 12 14 16 18 20 24 26 28 30 Time (years)
d)
o Current Balance 4.6 4.3 ii 않 3.4 3.3 26 24 1.8 16 1.4 ()않 0.6 0.4 0.2 0 0 1 02 04 0.5 09 Time log base 10) 1.1 1.4 1.5