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What is the formula to calculate the monthly payment (PMT) on a 20-year loan with principal amount \(P\), annual interest rate \(r\) (compounded monthly), and total number of monthly payments \(n\)?
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10. Time Value of Money
Time Value of Money Equations
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What is the future value of \$11 invested for 3 years at an annual interest rate of 5\% compounded annually?
A
\$12.76
B
\$13.00
C
\$11.55
D
\$12.10
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Step 1: Understand the formula for future value (FV) when interest is compounded annually. The formula is: FV = P × (1 + r)^n, where P is the principal amount, r is the annual interest rate (in decimal form), and n is the number of years.
Step 2: Identify the values given in the problem. Here, P = \$11, r = 5% (convert to decimal: 0.05), and n = 3 years.
Step 3: Substitute the values into the formula. Using MathML, the formula becomes:
Step 4: Perform the operations step by step. First, calculate (1 + r), then raise the result to the power of n, and finally multiply by P.
Step 5: Compare the calculated future value to the provided answer choices (\$12.76, \$13.00, \$11.55, \$12.10) to determine the correct answer.
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