21. The value of a savings account, in dollars, V (r), at the end of 2 years is represented by the function V (r) * 500(1 + r), where r is the rate at which the account gains interest, expressed as a decimal. What is the value of V (r) for r = 0.037
Answer: D
The value of V(r) for r = 0.037 is $509.00.
To find the value of V(r) when r = 0.037, we substitute this rate into the formula V(r) = 500(1 + r). This calculation yields V(0.037) = 500(1 + 0.037) = 500(1.037) = $509.00.
A) $530.45
This option is incorrect because it results from misunderstanding the calculations involved. The value of V(r) is derived directly from the formula, and substituting r = 0.037 does not yield this amount.
B) $501.06
This option is incorrect as well. A common error might lead to this incorrect calculation, but using the given formula directly shows that the correct value is higher than this amount.
C) $500.45
This option is also incorrect. It appears to be derived from an erroneous calculation, as the correct application of the formula gives a higher value than $500.45.
D) $509.00
This option is correct. By substituting r = 0.037 into the formula V(r) = 500(1 + r), we find that V(0.037) = 500(1.037) = $509.00, confirming that this is indeed the right answer.
Conclusion
The correct answer is definitively $509.00 as it directly follows from the application of the provided formula. All other options fail to accurately reflect the calculated value from the given rate, demonstrating a misunderstanding of the formula's use.