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Multiple Choice
What would be the future value of $150 after eight years if you earn 12\% interest per year, compounded annually?
A
$372.47
B
$420.00
C
$267.84
D
$299.12
Verified step by step guidance
1
Step 1: Understand the formula for future value with compound interest, which is \( FV = PV \times (1 + r)^n \), where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the annual interest rate, and \( n \) is the number of years.
Step 2: Identify the values given in the problem: \( PV = 150 \), \( r = 0.12 \) (12% annual interest rate), and \( n = 8 \) years.
Step 3: Substitute the values into the formula: \( FV = 150 \times (1 + 0.12)^8 \).
Step 4: Calculate \( (1 + 0.12) \), which equals \( 1.12 \), and then raise \( 1.12 \) to the power of 8 (\( 1.12^8 \)).
Step 5: Multiply the result of \( 1.12^8 \) by \( 150 \) to find the future value. Compare the calculated value to the provided answer choices to determine the correct one.