Master Determine the final value of a compound interest formula

The video tutorial explains how to calculate the final value in compound interest using different formulas. It covers the basic formula for compound interest, explains the importance of converting interest rates to decimal form, and demonstrates step-by-step calculations for different compounding frequencies, including monthly, yearly, and daily. The tutorial also introduces continuous compounding using the constant E and emphasizes the importance of following the order of operations and avoiding rounding errors during calculations.

What does the variable 'n' represent in the compound interest formula?

• The number of years

• The interest rate

• The number of compounding periods per year

• The initial investment amount

Why is it important to convert the interest rate to decimal form?

• To simplify the formula

• To avoid using fractions

• To ensure accurate calculations

• To make it easier to read

What is a common mistake students make when using the compound interest formula?

• Calculating the exponent before the base

• Not converting the interest rate to a percentage

• Using the wrong number of compounding periods

• Forgetting to multiply by the initial amount

In the example calculation, what is the final value if $2500 is invested at 8% interest compounded monthly for 10 years?

• $5,549.10

• $5,000.00

• $6,000.00

• $5,700.00

What is the shortcut formula for yearly compounding?

• F = P * (1 + r/n)^(n*t)

• F = P * (1 + r*t)

• F = P * (1 + r)^t

• F = P * (1 + r/n)^t

How many times is interest compounded in a year if it is compounded daily?

• 52 times

• 365 times

• 24 times

• 12 times

What is the final value of $1000 invested at 3% interest compounded daily for 5 years?

• $1,161.83

• $1,200.00

• $1,150.00

• $1,180.00

What is the formula for continuous compounding?

• F = P * e^(n*t)

• F = P * (1 + r)^t

• F = P * e^(r*t)

• F = P * (1 + r/n)^(n*t)

What is the approximate value of the mathematical constant 'e' used in continuous compounding?

• 1.62

• 2.71

• 3.14

• 1.41

If $7000 is invested at 5% interest compounded continuously for 20 years, what is the final value?

• $17,500.00

• $18,000.00

• $20,000.00

• $19,027.97