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

Rationale

The value of V(r) for r = 0.037 is $509.00.

To find V(r) for the given interest rate, we substitute r = 0.037 into the function V(r) = 500(1 + r). This calculation yields the correct value for V(r) at the end of 2 years.

A ($530.45) YOUR ANSWER

This choice assumes a higher interest outcome than calculated. The value of V(r) is derived from the equation 500(1 + 0.037), which does not support this total. Thus, this option inaccurately reflects the interest earned over 2 years.

B ($501.06) YOUR ANSWER

This value results from an incorrect application of the interest rate in the formula. Specifically, $501.06 would imply a calculation of V(r) using a miscalculated interest rate, leading to a total that does not align with the expected outcome of 500(1 + 0.037).

C ($500.45) YOUR ANSWER

This option incorrectly rounds the interest gained instead of calculating it accurately. The correct computation of V(r) should yield $509.00 when applying the interest rate properly, indicating that this value does not represent the correct final amount after 2 years.

D ($509.00) CORRECT

This choice correctly represents the value of the savings account after 2 years at an interest rate of 0.037. The calculation, V(r) = 500(1 + 0.037), results in $500 * 1.037 = $509.00, confirming this as the accurate value.

Conclusion

In conclusion, to determine the value of a savings account after 2 years, the correct calculation involves substituting the interest rate into the provided formula. The value of V(r) at an interest rate of 0.037 is indeed $509.00, while the other choices reflect incorrect computations of the interest or misinterpretations of the formula.

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

The value of V(r) for r = 0.037 is $509.00.

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