Question

question 4 (10 points)
match the compound interest formula (future value) variable with the definition.

number of times the
interest is compounded
each year 1. a
principal or initial amount
borrowed or invested 2. p
annual interest rate 3. r

1. n

future value 5. t
length of time in years for
the loan or investment

Explanation:

• For "Number of times the interest is compounded each year", the variable is \( n \) (option 4) as \( n \) represents compounding periods per year in compound interest formula \( A = P(1+\frac{r}{n})^{nt} \).
• For "Principal or initial amount borrowed or invested", the variable is \( P \) (option 2) as \( P \) is the principal in the compound interest formula.
• For "Annual interest rate", the variable is \( r \) (option 3) as \( r \) is the annual interest rate in the compound interest formula.
• For "Future value", the variable is \( A \) (option 1) as \( A \) is the future value in the compound interest formula.
• For "Length of time in years for the loan or investment", the variable is \( t \) (option 5) as \( t \) is the time in years in the compound interest formula.

Answer:

• Number of times the interest is compounded each year: 4. \( n \)
• Principal or initial amount borrowed or invested: 2. \( P \)
• Annual interest rate: 3. \( r \)
• Future value: 1. \( A \)
• Length of time in years for the loan or investment: 5. \( t \)