What is the effective yield (APY) if the Annual Percentage Rate (APR) is 7.64 percent and it is compounded quarterly?

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BlackTom AI · Accepted Answer

The problem asks for the APY (effective yield) when the APR is 7.64% compounded quarterly. To convert APR with quarterly compounding to APY, use the formula: APY = (1 + (APR / m))^m − 1, where m is the number of compounding periods per year.

First, identify the values: APR = 7.64% = 0.0764, m = 4 (quarterly compounding). Then compute the periodic rate: APR/m = 0.0764 / 4 = 0.0191, i.e., 1.91% per quarter.

Next, raise (1 + periodic rate) to the power m: (1 + 0.0191)^4 = (1.0191)^4. This requires either a calculator or stepwise approximation. One way is to square twice: (1.0191)^2 ≈ 1.03856481, and then (1.03856481)^2 ≈ 1.0786156. Therefore, APY ≈ 1.0786156 − 1 = 0.0786156, which is about 7.86156%.

Now evaluate each answer choice:
- 7.79 percent: This would correspond to a slightly smaller APY, implying either a lower compounding effect or a miscalculation in the exponent. Since our computed APY is around 7.86%, 7.79% is not consistent with quarterly compounding of 7.64% APR.
- 7.86 percent: This matches the calculated APY to two decimal places (7.8616% rounds to 7.86%). It reflects the compounded growth over the year given 4 periods per year at 1.91% each.
- 7.95 percent: This is higher than the computed value, suggesting a stronger effective yield than actually produced by the 7.64% APR with quarterly compounding. It would require a larger periodic rate or more compounding frequency.
- 7.98 percent: This is the highest option and likewise overstates the APY for the stated APR and quarterly compounding; it would result from an overestimation of the quarterly rate or an incorrect exponent application.

In summary, applying the standard APY formula with quarterly compounding precisely yields an APY about 7.8616%, which corresponds to the option around 7.86 percent. Other choices deviate from this value due to rounding differences or misapplication of the compounding effect.

MSB-250-300-002 Proctored Midcourse Exam 1

What is the effective yield (APY) if the Annual Percentage Rate (APR) is 7.64 percent and it is compounded quarterly?

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MSB-250-300-002 Proctored Midcourse Exam 1

What is the effective yield (APY) if the Annual Percentage Rate (APR) is 7.64 percent and it is compounded quarterly?

View Explanation

Log in for full answers

Similar Questions

Part 1Consider a twominus−year ​investment: Given a constant and positive interest​ rate, the interest earned in the second year will be greater than the interest earned in the first year​ (assuming annual​ compounding). Part 1 True False

If Jack and Jill deposit $1,000 into a savings account that earns 4.5% annual interest (compounded monthly), how long will it take for their money to double to $2,000?

How much will you get back on a five year investment of $100 that pays 5% interest per year?

If you deposit $10,000 in an account with an annual rate of 9% compounded semiannually, how long will it take for you to have $2,000,000 in the account?

In order to determine the future value of some lump sum, we must use the process of ________.

With compound interest, the investor earns interest on the principal amount invested plus interest on accumulated interest. Which of the following compounding frequencies would yield the investor the greatest ending balance assuming all else is equal?

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