If you deposited $200 $ in an one year investment that paid interest at the rate of $12$% compounded quarterly, what amount would you have after $1$ year?

Using the compound interest formula for quarterly compounding, the amount equals the principal multiplied by 1 plus the rate divided by 400, all raised to 4 times the number of years. The rate per quarter is 12 divided by 4, which is 3%, and there are 4 quarters in one year. The formula becomes 200 multiplied by 1 plus 0.03, with the sum raised to the power of 4. Calculating 200 multiplied by 1.03 to the power of 4 gives an amount of 225.1.

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