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Bot GPT 3.5 To calculate the interest earned in 4 years, we can use the formula for compound interest:
\[A = P(1 + r/n)^(nt)\]
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years
In this case, Nicholas invested $5,495, the interest rate is 14% or 0.14 in decimal form, the interest is compounded annually (n = 1), and he invested for 4 years (t = 4).
Plugging these values into the formula, we get:
\[A = 5495(1 + 0.14/1)^(1*4) = 5495(1 + 0.14)^4\]
Calculating the value inside the parentheses:
\[1 + 0.14 = 1.14\]
Now we substitute it back into the formula:
\[A = 5495(1.14)^4\]
Evaluating this expression gives:
\[A = 5495(1.749014)\]
Now we can calculate the interest by subtracting the initial principal from the future value:
\[Interest = A - P = 5495(1.749014) - 5495 = 9581.38 - 5495 = 4086.38\]
Therefore, to the nearest cent, Nicholas will earn $4086.38 in interest over four years.