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A company had a profit of $45,000 in its first year of operation. Each successive year, it had a 6% raise in its profit. What would be the total profit of the company over a period of 15 years?

Respuesta :

CastleRook
Given that the companies profits growth at the rate of 6%, the profits after 15 years will be calculated using the formula:
A=P(1+r/100)^n
P=initial amount
r=rate
n=time
thus plugging in the values we obtain:
A=45000(1+6/100)^15
A=45000(1.06)^15
A=$107, 845.12
Thus the profit after 15 years was $107, 845.12

Answer:

Step-by-step explanation:

Note that the profit of the company's second year is 45000(1.06)^1. Then, each year after that, it's profit is 45000(1.06)^2, 45000(1.06)^3, 45000(1.06)^4, and so on.

After 15 years, its profit is the sum:

45000 + 45000(1.06)^1 + ... + 45000(1.06)^13 + 45000(1.06)^14.

This is a geometric series that has a first term of 45000, a common ratio of 1.06, and 15 terms. Therefore, this sum evaluates to:

45000[1 - (1.06)^15]/(1 - 1.06), by the sum of a geometric series formula

≈ $1047418.65.

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