Let t be the time it takes to earn $1000 in interest
Interest=1000
Hence,
1000=10000*(1+2.2%)^t-10000
=>1.022^t=1.1
=>t*ln1.022=ln1.1
=>t=ln(1.1)/ln(1.022)
=>t=4.37976315
Hence, it will take 4.37976315 years
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