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How to Calculate Interest on Top of Interest

When you receive interest from the bank, you get more money. And when you earn interest on the interest you earned earlier, this makes the dollar amounts grow even faster. Here’s an example:

Bethany placed $9,500 in a one-year CD that paid 4% interest. The next year, she rolled this over into a bond that paid 6% per year. How much did Bethany earn on her investment in those two years?

This problem involves interest, so it’s another problem in percent increase, only this time, you have to deal with two transactions. Take them one at a time.

The first transaction is a percent increase of 4% on $9,500. The following word equation makes sense:

Money after first year = 100% of initial deposit + 4% of initial deposit

Money after first year = (100% + 4%) of $9,500 = 104% of $9,500

Now change the percent to a decimal and the word of to a multiplication sign:

Money after first year = 1.04 $9,500

Multiplication gives you this result:

Money after first year = $9,880

At this point, you’re ready for the second transaction. This is a percent increase of 6% on $9,880:

Final amount = 106% of $9,880

Again, change the percent to a decimal and the word of to a multiplication sign:

Final amount = 1.06 $9,880 = $10,472.80

Then subtract the initial deposit from the final amount:

Earnings = final amount – initial deposit = $10,472.80 – $9,500 = $972.80

So Bethany earned $972.80 on her investment.

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