Answer:
The total amount received is: $1906650
Step-by-step explanation:
Given
[tex]a = \$57000[/tex] --- initial
[tex]b = 1\%[/tex] --- rate
[tex]n = 29[/tex] --- time
Required
Determine the total amount at the end of 29 years
The given question is an illustration of geometric progression, and we are to solve for the sum of the first n terms
Where [tex]n = 29[/tex]
[tex]r = 1 + b[/tex]
[tex]r = 1 + 1\%[/tex]
Express percentage as decimal
[tex]r = 1 + 0.01[/tex]
[tex]r = 1.01[/tex]
The required is the calculated using:
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
So, we have:
[tex]S_n = \frac{57000 * (1.01^{29} - 1)}{1.01 - 1}[/tex]
[tex]S_n = \frac{57000 * (1.3345- 1)}{0.01}[/tex]
[tex]S_n = \frac{57000 * 0.3345}{0.01}[/tex]
[tex]S_n = \frac{19066.5}{0.01}[/tex]
[tex]S_n = 1906650[/tex]
The total amount received is: $1906650
