Multiple Choice
Which of the following best defines the future value in the context of the time value of money?
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10. Time Value of Money
Time Value of Money Equations
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Raul deposited $5,000 into a savings account that pays an annual interest rate of 6%, compounded annually. After 3 years, how much interest did Raul earn through compound interest in his savings account?
A
$1,200.00
B
$955.08
C
$1,000.00
D
$900.00
Verified step by step guidance1
Step 1: Understand the formula for compound interest. The formula is: \( A = P(1 + r)^t \), where \( A \) is the total amount after interest, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), and \( t \) is the time in years.
Step 2: Identify the values given in the problem. Here, \( P = 5000 \), \( r = 0.06 \) (since 6% = 0.06), and \( t = 3 \). Substitute these values into the formula.
Step 3: Calculate the total amount \( A \) after 3 years using the formula \( A = P(1 + r)^t \). This involves first adding \( 1 + r \), then raising the result to the power of \( t \), and finally multiplying by \( P \).
Step 4: Determine the compound interest earned by subtracting the principal \( P \) from the total amount \( A \). The formula for compound interest is \( ext{Interest} = A - P \).
Step 5: Compare the calculated interest to the options provided in the problem to identify the correct answer.
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