Effective Interest Rate Concepts

This video tutorial explains the concept of the effective rate of interest, also known as effective yield. It covers the formulas for calculating effective interest rates for both compounded and continuous interest. The video derives these formulas and provides examples to illustrate how to calculate the effective interest rate for different scenarios. The effective interest rate is the equivalent annual simple interest rate that yields the same return after one year as an account paying compounded or continuous interest.

What is the primary goal of learning about the effective rate of interest?

• To understand the concept of inflation.

• To understand how to calculate simple interest.

• To know the formula for effective interest rate for compounded and continuous interest.

• To learn about the history of interest rates.

Which formula represents the effective interest rate for compounded interest?

• R sub E = (1 + R)^T

• R sub E = P(1 + RT)

• R sub E = (1 + R/N)^N - 1

• R sub E = E to the R - 1

In the derivation of the compounded interest formula, what is the value of T?

• R

• 0

• N

• 1

What is the effective interest rate formula for continuous interest?

• R sub E = (1 + R/N)^N - 1

• R sub E = E to the R - 1

• R sub E = (1 + R)^T

• R sub E = P(1 + RT)

What is the first step in deriving the formula for continuous interest?

• Calculate the number of compounding periods.

• Set the simple interest formula equal to the compounded interest formula.

• Convert the interest rate to a percentage.

• Set the simple interest formula equal to the continuous interest formula.

How is the effective interest rate for a 4% quarterly compounded interest calculated?

• By using the formula R sub E = (1 + R/N)^N - 1

• By dividing the interest rate by 4

• By using the formula R sub E = E to the R - 1

• By multiplying the interest rate by 4

What is the effective interest rate for an account paying 4% continuous interest?

• 3.92%

• 4.00%

• 4.08%

• 4.06%

Why is the effective interest rate for continuous interest slightly higher than for compounded interest?

• Because compounded interest is calculated annually.

• Because continuous interest has a lower rate.

• Because compounded interest is more complex.

• Because continuous interest compounds more frequently.

What is the decimal approximation of the effective interest rate for 4% quarterly compounded interest?

• 0.0406

• 0.0398

• 0.0408

• 0.0410

How do you convert a decimal approximation of an interest rate to a percentage?

• Subtract 100

• Multiply by 100

• Divide by 100

• Add 100