Continuously Compounded Math

R annual interest rate.

Continuously compounded math. 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. The formula for continuously compounded interest is defined as. An investor is given the option of investing 1 000 for 5 years in two deposit options. Interest accrued total balance starting balance 15464 9890 5574.

Consider the following example. T time 60 months 5 years. General compound interest principal 1 annual interest rate n n time. N is the number of times interest is compounded in a year.

You invest some money the principal in a bank which pays interest. P principle starting balance 9890. Total balance p e rt. We continue the discussion that was started in section 3 1.

Continuously compounded interest is a great thing when you are earning it. How the continuous compounding formula is derived 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. A woman deposits 5 000 into a savings account with continuously compounded interest at an annual rate of 4 5. When n or the number of times compounded is infinite the formula can be rewritten as.

R interest rate 9. After a specified time the compounding period you add in the interest that has been earned on the principal. P principal dollars invested. 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.

This formula makes use of the mathemetical constant e. Total balance principle e rate time 9890e 9 100 5 9890e 0 45 9890 2 7 0 45 15464. Learn more about our online math practice software. It is an extreme case of compounding since most interest is compounded on a monthly quarterly or semiannual basis.

T term of investment in years example. 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. Instead of using the number of years in the equation continuous compounding uses an exponential constant to represent the infinite number of periods. Simple and compound interest.

A p e r t r 4 100 0 04. To calculate continuously compounded interest use the formula below. Continuous compounding is the mathematical limit that compound interest can reach if it s calculated and reinvested into an account s balance over a theoretically infinite number of periods.