Continuous compounding question - have I solved it correctly? I suppose my total capital is 2100?

Question

Take the current amount you have in your checking or savings account. Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with and interest rate of 4.5%. Calculate how much interest you would earn with each option over five years time with continuous compounding.
A = Ce^RT My total money in the bank is 2100 dollars in round figures. Since the formula for the continuous compounding is A=Ce^RT where C is the initial deposit or capital, T for time, R is the rate of interest and A will be the final amount.
Capital = 2100, Interest Rate ( R) = 2% Time (T) = 5 years, e = 2.7182818284
When money kept for five years in a savings account with a 2% interest rate:
By using the values into formula:= 2100 e ^(0.02*5) = 2318.57
Interest earned = 2318.57 – 2100 = 218.57 dollars
Five year certificate of deposit with interest rate of 4.5%.So A = Ce^RT 2100e^4.5*5=2680.19 - 2100=$516.98

Answer 1

The term 'Continuous Compounding' is not one I have come across before ..

In this context, I am going to assume in means 'Interest paid Daily' ... i.e. at the end of each day, interest is added to the account .. and thus, on the next day, you get 'interest on the interest' .. and so on..

The formula does not seem to be quite right .. the product RT is plainly the same irrespective of when the interest is paid

For example, if you have 2% interest paid annually for 5 years RT = .1 ....... and after 5 years you have 2318.57 (as per your calculation)

On the other hand, if you have 2/12 = .01666r % Interest paid monthly for 5x12 = 60 months, RT is still .1 .. BUT if you ACTUALLY spreadsheet this case for 60 months, you end up with 2320.67

If you do it for 1821 days (I've included 1 leap year), you end up with 2320.98 ...

Answer 2

Yes you have.
Give yourself 10 points