I already have the answer solved... I just dont understand this last part: \"(1

Question

I already have the answer solved... I just dont understand this last part: "(1 + i)^15 = 10 – 1; (100.6666) – 1; r = 1.1659 – 1; Rate = 16.59% ". how does the 10 gets those ^6 (sixth powers) ?

At what rate must $4,000 be compounded annually for it to increase to $40,000 in 15 years? (Do not round the intermediate calculations. Round the final answer to the nearest two decimals.) Entry field with correct answer

Correct answer. Future value = Present value × (1 + interest rate)n; $40,000 = $4,000 × (1 + i)^15; (1 + i)^15= $40,000 / $4,000; (1 + i)^15 = 10 – 1; (1 + i)^15 = 10 – 1; (100.6666) – 1; r = 1.1659 – 1; Rate = 16.59%

A. 16.59%

Explanation / Answer

The formula for annual compound interest is A = P (1 + r/n) ^ nt:

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

Using the above formulae; the interest is compounded.

Coming to your doubt;

Here, you need to compute the “r”, that is the rate of interest.

The power of 15 is the number of years or the time taken.

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