Multiple Choice
Interest that builds on the principal and the interest already gained is called:
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10. Time Value of Money
Time Value of Money Equations
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
If you borrow \$20,000 for 5 years at an annual interest rate of 8\% compounded monthly, what would the monthly payment be?
A
\$405.53
B
\$405.53
C
\$405.98
D
\$405.34
Verified step by step guidance1
Step 1: Identify the formula for calculating the monthly payment for a loan. The formula is: \( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \), where \( M \) is the monthly payment, \( P \) is the loan principal, \( r \) is the monthly interest rate, and \( n \) is the total number of payments.
Step 2: Convert the annual interest rate to a monthly interest rate. Divide the annual interest rate (8\%) by 12 months: \( r = \frac{0.08}{12} \).
Step 3: Calculate the total number of payments. Multiply the number of years (5 years) by 12 months per year: \( n = 5 \cdot 12 \).
Step 4: Substitute the values into the formula. Use \( P = 20000 \), \( r \) (monthly interest rate from Step 2), and \( n \) (total number of payments from Step 3) in the formula \( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \).
Step 5: Simplify the formula step by step to calculate the monthly payment. Ensure all calculations are performed accurately, including exponentiation and division.
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