Multiple Choice
Which time value of money function calculates the total principal paid through a specified number of payments?
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10. Time Value of Money
Time Value of Money Equations
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How many years will it take for \$20 to grow to \$100 if the simple interest rate is 4\% per year?
A
20 years
B
100 years
C
80 years
D
40 years
Verified step by step guidance1
Step 1: Understand the formula for simple interest, which is \( I = P \cdot r \cdot t \), where \( I \) is the interest earned, \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years.
Step 2: Calculate the total interest needed for the principal \( P = 20 \) to grow to \( 100 \). The total interest \( I \) is \( 100 - 20 = 80 \).
Step 3: Rearrange the simple interest formula to solve for \( t \): \( t = \frac{I}{P \cdot r} \). Substitute \( I = 80 \), \( P = 20 \), and \( r = 0.04 \) into the formula.
Step 4: Perform the division and multiplication operations to calculate \( t \). Specifically, divide \( I \) by \( P \cdot r \): \( t = \frac{80}{20 \cdot 0.04} \).
Step 5: Interpret the result for \( t \) to determine the number of years it will take for \$20 to grow to \$100 at a simple interest rate of 4\% per year.
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