Part (a)
Answer: y = 5000(1.016)^x
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Explanation:
You use the compound interest formula
A = P(1 + r/n)^(n*t)
where
- A = final amount after t years
- P = amount deposited (principal) = 5000
- r = decimal form of interest rate = 0.016
- n = number of times we compound per year = 1
- t = number of years = x, some unknown number
After plugging those values in, you would go from A = P(1 + r/n)^(n*t) to
A = P(1 + r/n)^(n*t)
A = 5000(1 + 0.016/1)^(1*x)
A = 5000(1.016)^x
Since you're using x for the input, it's possible your teacher wants you to use y for the output. So replace A with y to get y = 5000(1.016)^x
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Part (b)
Answer: 6344.18 dollars
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Explanation:
Plug x = 15 into the equation we found back in part (a). Use your calculator to simplify. Round to the nearest hundredth which is rounding to the nearest penny.
y = 5000(1.016)^x
y = 5000(1.016)^15
y = 6344.1818561953
y = 6344.18
