Continuous Compound Interest Sample Problems

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Continuous Compound Interest

In this topic, we use the same terms as the terms for simple interest.
To review the terms for simple interest, see here.
To review compound interest, see here.

Continuous compound interest is a form of compound interest where the interst is compounded in very very small time periods, or continuously.

The formula for the total ending balance after a certain amount of time using continuous compound interest is

Total Balance = Principle × e^(Rate)(Time) = Pe^rt
where e ≈ 2.7183...

Example 1:

Answer the following questions involving continuously compounded interest. Input all answers to the nearest dollar. Use 2.7 as the value for e.

Interest Rate: 5% per year
Starting Balance: $2160
Time Passed: 13 years
What is the new total balance?
How much interest has accrued if calculated as continuously compounded interest?

Total balance:
Interest:

Calculate the total balance first.
Then find the amount of interest earned.

Total balance = Pe^rt

= ($2160)e^(0.05)(13)

= ($2160)(2.7)^0.65

= $4119.46

Continuous Compound Interest = Total Balance - Principle

= $4119.46 - $2160

= $1959.46

Rounding to the nearest dollar, the answer is Total balance: Interest:

Total balance	=	Pe^rt
	=	($2160)e^(0.05)(13)
	=	($2160)(2.7)^0.65
	=	$4119.46

Continuous Compound Interest	=	Total Balance - Principle
	=	$4119.46 - $2160
	=	$1959.46