Formula For Continuous Compound Interest Math

Pv fv 1 r n. The continuous compounding formula can be found by first looking at the compound interest formula where n is the number of times compounded t is time and r is the rate. This is not actually possible but continuous compounding is well defined nevertheless as the upper bound of regular compound interest the formula given below is sometimes called the shampoo formula pert.

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Fv future value pv present value r interest rate as a decimal value and.

Formula for continuous compound interest math. Interest that is hypothetically computed and added to the balance of an account every instant. N is the number of times interest is compounded in a year. Fv pv 1 r n. Consider the following example.

General compound interest principal 1 annual interest rate n n time. This formula makes use of the mathemetical constant e. The basic formula for compound interest is. If it took 6 years for your initial amount compounded continuously at an interest rate of 4 and you ended up with 11 44 then your initial principal was 9.

How much money will she have after five years. An investor is given the option of investing 1 000 for 5 years in two deposit options. A p e r t 11 44 p e 0 04 6 11 44 p e 0 24 11 44 e 0 24 p 9 p. In the formula a represents the final amount in the account that starts with an initial principal p using interest rate r for t years.

Finds the future value where. A woman deposits 5 000 into a savings account with continuously compounded interest at an annual rate of 4 5. N number of periods. When n or the number of times compounded is infinite the formula can be rewritten as.

Continuously compounded interest is a great thing when you are earning it. To calculate continuously compounded interest use the formula below. And by rearranging that formula see compound interest formula derivation we can find any value when we know the other three.