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Chapter 8: Problem 57

A bank offers a money market account paying \(4.5 \%\) interest compounded semiannually. A competing bank offers a money market account paying \(4.4 \%\) interest compounded daily. Which account is the better investment?

Short Answer

Expert verified
To determine the better investment, compare the APYs of both accounts. The account with the higher APY provides a higher yield.

Step by step solution

01

Calculate the Annual Percentage Yield (APY) for the semiannually compounded account

The formula for APY is \( APY = (1 + r/n) ^ {n*t} - 1\), where: r is the nominal interest rate (as a decimal), n is the number of compounding periods in a year, and t is the time in years. Since the time for both accounts is not specified, we can assume that t = 1 year for easier comparison. Thus the APY calculation for the first account becomes: \( APY = (1 + 0.045/2) ^ {2*1} - 1 \).
02

Calculate the APY for the daily compounded account

Applying the same formula as above, but now with the compounding done daily (n = 365), the APY calculation for the second account will be: \( APY = (1 + 0.044/365) ^ {365*1} - 1 \).
03

Compare the APYs of both accounts

After calculating both APYs, the best investment would be the bank account with the highest yield, i.e. the one with the highest APY value.

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