Question 558613
With annual compounding, the $10,000 deposit would earn $400 in interest the first year. (A $100 interest would be earned each quarter, but that extra money would not be accruing extra interest during the first year).
At the beginning of the second year, the balance would be $10,400, and interest would be calculated based on that new balance for the whole second year.
For each of the 10 years the balance at the beginning of the year would be multiplied times 1.04 by the end of the year: each $100 would turn into $104.
{{{1.04=(100+4)/100}}}
After 10 years the balance would be
${{{10000*1.04^10}}} = ${{{14802.44}}}
If the interest were compounded quarterly, after 3 month, you would have an extra $100, just like before, for a total of $10,100, but interest would start accruing on the whole $10,100 for the second quarter. So, during the second quarter you would get another $100 in interest from the initial $10,000, plus an extra $1 from the interest on the $100 earned on the first quarter. During the third quarter, you would get interest on the whole $10,201. You would get another $100 from the initial $10,000, but you would also earn $2.01 on the $201 interest earned in the previous 2 quarters. Each quarter, it would get better. The balance at the beginning of the quarter would be multiplied by 1.01 at the end of the quarter. At the end of the first year, the balance would be
${{{10000*1.01^4}}} = ${{{10406.04}}}.
Because of the quarterly compounding, you would be $6.04 ahead after just one year.
After 10 years, which is 40 quarters, the final balance would be
${{{10000*1.01^40}}} = ${{{14888.64}}}.
That's an extra $86.20, due to the interest generated on the interest from the previous quarters.