Answer:
Account 1 has the highest effective annual interest rate (0.042666142)
Step-by-step explanation:
Hi, to answer this question we have to apply the Effective Annual Interest Rate formula:
EAIR = [(1+r/n)^n ]-1
Where:
r = nominal interest rate
n = number of periods
If interest is compounded annually, then n = 1; if semi-annually, then n = 2; quarterly, then n = 4; monthly, then n = 12
SO:
Account 1: Interest is compounded quarterly at an annual rate of 4.20%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.20/100)/4)^4 ]-1 = 0.042666142
Account 2: Interest is compounded monthly at an annual rate of 4.15%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.15/100)/12)^12 ]-1 =0.042298535
Account 3: Interest is compounded semiannually at an annual rate of 4.10%
EAIR = [(1+r/n)^n ]-1 = [(1+(4.10/100)/2)^2]-1 = 0.04142025
Account 4: Interest is compounded annually at a rate of 4.25%.
EAIR = [(1+r/n)^n ]-1 = [(1+(4.25/100)/1)^1 ]-1 = 0.0425
Since:
0.042666142 (1) < 0.0425 (4) < 0.042298535(2) <0.041420258(3)
Account 1 has the highest effective annual interest rate 0.042666142
feet. Using the distributive property, we can simplify this to:
