F=P*( 1+i)^n
F=A(( 1+i)^n- 1)/i
P=F/( 1+i)^n
p=a(( 1+i)^n- 1)/(i( 1+i)^n）
A=Fi/(( 1+i)^n- 1）
a=p(i( 1+i)^n)/(( 1+i)^n- 1）
F: future value, or future value, that is, the sum of principal and interest at the end of the period.
P: present value, or beginning amount.
A: Annuity or equivalent value.
Interest rate or discount rate
N: Number of interest-bearing periods
The characteristic of compound interest calculation is that the sum of the principal and interest at the end of the previous period is taken as the principal of the next period, and the amount of the principal of each period is different when calculating. The formula for calculating the principal and interest of compound interest is f = p (1+I) n.
The calculation of compound interest can be divided into intermittent compound interest and continuous compound interest The method of calculating compound interest on schedule (such as year, half year, quarter, month or day) is intermittent compound interest; The method of calculating compound interest instantly is continuous compound interest. In practical application, the calculation method of discontinuous compound interest is generally adopted.
Present value of compound interest
The present value of compound interest refers to the principal that must be invested in order to reach a certain amount of funds in the future under the condition of calculating compound interest. The so-called compound interest, also known as rolling interest, refers to the method of making a new round of investment with interest after the deposit or investment is rewarded.
Compound interest final value
The final value of compound interest refers to the sum of principal plus interest after the principal receives interest within the agreed period.
Step 2: Example
For example, if the principal is 50,000 yuan, the interest rate or investment return rate is 3%, and the investment period is 30 years, the principal+interest income obtained after 30 years is calculated according to the compound interest formula: 50,000× (65,438+0+3%) 30.
Because the inflation rate and interest rate are closely related, just like the two sides of a coin, the formula for calculating the final compound interest value can also be used to calculate the actual value of a specific fund in different years. Just change the interest rate in the formula to the inflation rate.
For example, to raise a pension of 3 million yuan after 30 years, assuming the average annual rate of return is 3%, the principal that must be invested is 3,000,000×1(1+3%) 30.
Interest is settled once a year (at a single interest rate), and then the principal and interest are merged into the principal of the next year. This figure will be used as the principal when the interest is settled next year. Compound interest is more than single interest.
Extended data:
Application of compound interest calculation;
(1) Calculate the final value of principal and interest of multiple equal investments.
Make equal investment in P at the beginning of each interest period, and the final value at the end of n interest periods is: VC = P (1+i) × [(1+i) n-1]/i.
Obviously, when n= 1, Vc = p×( 1+I), that is, at the end of the first interest period, the final value only includes the equal amount of investment and its interest. When n=2, Vc = p×(2+3×I+I×I), that is, in the second interest period.
In construction projects, bidders need to borrow money for many times or use their own funds to invest. Assuming that the amount invested each time is the same and the interval is the same, the project payment M can only be obtained after the project acceptance. if VC》； M, the bidder should not bid.
(2) calculating a plurality of equal payment values
Assuming that the amount recovered each time is the same and the interval is the same, the calculation formula is: VC/n = p× (1+I) n× I/[(1+I) n-1].
Obviously, when n= 1 and V = p×( 1+I), that is, at the end of the first interest period, the investment will be fully recovered. In the construction project, after the bidder has invested P at one time, it is assumed that the tenderer will repay the project payment M of the winning bidder every once in a while, if VC/N; M, the bidder should not bid.