# Compound Interest

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. I’m going to do this for my checking and savings account amount Checking Account

A = Ce^RT My total money in the checking account is 2100 dollars 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

Savings Account = P*e^rt = Pe^(0.02*5) = Pe^0.1 = 1.105171P Therefore, Interest = A - P = 0.105171P

Amount with certificate of deposit account = P*e^rt = Pe^(0.045*5) = Pe^0.225 = 1.252323P

Therefore, Interest = A - P = 0.252323P

A = 10,000e^(.02*5) = $11051.71 return stocks I have the...

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