What annual interest rate, compounded annually, will cause an original deposit of $400 to grow to $625, after 7 years?
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A. B. C. D. E.B
On the BAII Plus, press 7 N, 400 PV, 0 PMT, 625 +/- FV, then CPT I/Y. On the HP12C, press 7 n, 400 PV, 0 PMT, 625 CHS FV, then press i. Make sure the BAII
Plus has the P/Y value set to 1.
To solve this problem, we can use the formula for compound interest:
Future Value (FV) = Present Value (PV) × (1 + Interest Rate)^Number of Periods
In this case, the original deposit (PV) is $400, and we want it to grow to $625 after 7 years. We need to find the annual interest rate.
Plugging in the values into the formula, we have:
$625 = $400 × (1 + Interest Rate)^7
To solve for the interest rate, we need to isolate it on one side of the equation. Let's divide both sides by $400:
$625 / $400 = (1 + Interest Rate)^7
1.5625 = (1 + Interest Rate)^7
Now, let's take the seventh root of both sides of the equation to get rid of the exponent:
(1.5625)^(1/7) = 1 + Interest Rate
1.0769 = 1 + Interest Rate
Subtracting 1 from both sides, we get:
Interest Rate = 1.0769 - 1
Interest Rate = 0.0769
To express this as a percentage, we multiply by 100:
Interest Rate = 0.0769 × 100
Interest Rate = 7.69%
Therefore, the correct answer is not provided in the answer choices. However, the closest option is C. 7.27%. Keep in mind that this may be an error in the question or answer choices provided by the test prep provider. It's important to verify and consult the official study materials or contact the provider for clarification if necessary.