A deposit account pays 12 per annum with continuous compound

A deposit account pays 12% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?

***Can you please explain step by step on how to do this question*** and please show formulas used so I can understand how to do it on my own. thank you.

Solution

Amount = Principal X e ^ rt

1. Principal is the Deposit or Borrowing for which you want to Calculate in this Case $10,000

2. r = Rate of Interest = 12 % per annum

3. t = Time for which you want to calculate in this case , t = 1 quarter = 3/12 = 1/ 4

4. Amount = $ 10,000 X e ^ 0.12x1/4

= $ 10,000 X e ^ 0.03

= $ 10,000 X 1.03045

= $ 10,304.5

5. Interest Paid = Amount - Principal

= $ 10,304.5 - 10,000

= $ 304.5

e^x ( in this case 0.03 ) is available from Statistical tables.