Example:

If the continuous compound interest rate is 7%, the effective annual interest rate = E (7%)- 1 = 7.25%.

If the effective annual interest rate paid by the bank to you is 8.75%, how much continuous compound interest do other bank competitors need to pay to attract investment?

The effective annual interest rate is 8.75%, so continuous compound interest =ln( 1+8.75%)=8.39%, which means that other bank competitors need to pay no less than 8.39% continuous compound interest to attract investors.

E is an acyclic number in mathematics, and e is also the base of common logarithm.

Continuous compound interest formula

I. Nominal interest rate, real interest rate and continuous compound interest When the interest period is not one year, how to convert it into annual interest rate? In general compound interest calculation and technical and economic analysis, the given or adopted interest rate is generally the annual interest rate, that is, the time unit of interest rate is one year, unless otherwise specified, the interest period is also one year, that is, the interest is calculated once a year. In practice, the given interest rate is still the annual interest rate.

Because the interest period may be a shorter time unit than a year, such as half a year, a quarter, a month, a week or a day. , the number of interest-bearing times in a year is 2, 4, 12, 52, or 365, etc. In this way, interest is calculated more than once a year, and every time interest is calculated under the condition of compound interest, some new interest will be generated, so the actual interest rate will be different (because the number of interest calculations is different).

If the interest is calculated monthly, the monthly interest rate is 1%, which is usually called "the annual interest rate is 12%, and the interest is calculated once a month". The annual interest rate of 12% is called "nominal interest rate". In other words, the nominal interest rate is equal to the product of the interest rate per interest period and the number of interest periods per year. If calculated by simple interest, the nominal interest rate is consistent with the real interest rate. However, if calculated by compound interest, the actual annual interest rate of the above "annual interest rate 12%" is not equal to the nominal interest rate, but should be slightly higher than 12%. 12.68%

For example, the principal 1000 yuan and the annual interest rate 12. If the interest is calculated once a year, the sum of the principal and interest after one year is:

f， 1000，( 1，0. 12， 12) 12， 1 126。 8 yuan

The actual annual interest rate I is: I = (1126.8-1000)/1000 *100%-12.68%.

This 12.68% is the real interest rate. In the above example, if calculated by continuous compound interest, the real interest rate is: I = e 0.12-1.1257-1=12.75%, assuming the nominal interest rate is R.