Understanding Compounded Interest and APY

The video tutorial explains how to calculate the balance of a savings account with a 4.7% annual percentage rate compounded quarterly. It demonstrates the use of the compound interest formula to determine the account balance after one year. Additionally, it covers the calculation of the annual percentage yield (APY) using two different methods, highlighting the slight differences in results due to rounding. The tutorial aims to help viewers understand the relationship between APR, compound interest, and APY.

What is the annual interest rate for the savings account?

• 5.0%

• 4.5%

• 4.7%

• 5.2%

How often is the interest compounded in Marie's savings account?

• Semi-annually

• Monthly

• Quarterly

• Annually

What is the initial deposit amount made by Marie?

• $4,500

• $4,000

• $4,700

• $5,000

Which formula is used to calculate the balance after one year with compounded interest?

• A = P(1 + r)^t

• A = P(1 + rt)

• A = P(1 + r/n)^(nt)

• A = P(1 + n/r)^(rt)

What is the account balance after one year?

• $4,750.00

• $4,715.26

• $4,700.00

• $4,800.00

What does APY stand for?

• Annual Profit Year

• Annual Percentage Year

• Annual Profit Yield

• Annual Percentage Yield

How is the APY calculated using the first formula?

• Initial deposit plus balance after one year

• Balance after one year divided by initial deposit

• Initial deposit minus balance after one year

• Balance after one year minus initial deposit, divided by initial deposit

What is the APY calculated using the first formula?

• 4.70%

• 4.75%

• 4.80%

• 4.78%

What is the second formula used to calculate APY?

• APY = (1 + r/n)^t - 1

• APY = (1 + n/r)^r - 1

• APY = (1 + r)^n - 1

• APY = (1 + r/n)^n - 1

Why might there be a slight difference between the two APY calculations?

• Due to rounding of the balance after one year

• Due to incorrect initial deposit

• Due to different interest rates

• Due to different compounding periods