Question

Which of the following statements is true—assuming that no additional deposits or withdrawals are made?

(A) An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time.
(B) An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time.

Answer 1

Using the compound interest formula, it can be deduced that a $50 investment at 5% annual interest will grow to $63.81 after five years, while a $25 investment at 10% annual interest will grow to $40.26, making statement (A) the true one.

Step-by-step explanation:

The question which of the following statements is true—assuming that no additional deposits or withdrawals are made—focuses on determining which investment scenario would end with a higher value after five years: $50 invested at an annual rate of 5% or $25 invested at an annual rate of 10%. We have to calculate the future value of both investments using the formula for compound interest:
For the $50 investment at 5%, the future value (FV) is calculated as follows:
FV = $50 × (1 + 0.05)5 = $50 × 1.2763 = $63.81

For the $25 investment at 10%, the future value (FV) is calculated as follows:
FV = $25 × (1 + 0.10)5 = $25 × 1.6105 = $40.26

After comparing the future values, we can conclude that (A) An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time.

Answer 2

The answer is the (A)

Step-by-step explanation:

In the exercise you have to apply the equation of compound interest rate to the two scenarios or options that give the exercise to determine which options is greater.

Future Value = Amount o money *(1+ interest rate)^(n)

Option(A) = $50*((1+5%)^(5))

Option(A) = $63,81

Option(B) = $25*((1+5%)^(5))

Option(B) = $40,26

After do the two calculus, you can determine that the answer is A because in the 5 years that investment generate a higher value that B option , according with the future value equation.