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IRS.gov Website
Publication 970
taxmap/pubs/p970-040.htm#en_us_publink1000178623

Figuring the Tax-Free Amount(p63)

rule
If the total you receive when you cash in the bonds is not more than the adjusted qualified education expenses for the year, all of the interest on the bonds may be tax free. However, if the total you receive when you cash in the bonds is more than the adjusted expenses, only part of the interest may be tax free.
To determine the tax-free amount, multiply the interest part of the proceeds by a fraction. The numerator (top part) of the fraction is the adjusted qualified education expenses (AQEE) you paid during the year. The denominator (bottom part) of the fraction is the total proceeds you received during the year.
taxmap/pubs/p970-040.htm#en_us_publink1000178624

Example.(p63)

In February 2013, Mark and Joan Washington, a married couple, cashed a qualified series EE U.S. savings bond. They received proceeds of $9,000, representing principal of $6,000 and interest of $3,000. In 2013, they paid $7,650 of their daughter's college tuition. They are not claiming an American opportunity or lifetime learning credit for those expenses, and their daughter does not have any tax-free educational assistance. Their MAGI for 2013 was $80,000.
 $3,000
interest
×  $7,650 AQEE 
$9,000 proceeds
=$2,550
tax-free
interest
 
They can exclude $2,550 of interest in 2013. They must pay tax on the remaining $450 ($3,000 − $2,550) interest.
taxmap/pubs/p970-040.htm#en_us_publink1000178626

Effect of the Amount of Your Income on the Amount of Your Exclusion(p63)

rule
The amount of your interest exclusion is gradually reduced (phased out) based on your MAGI and filing status.