Compound interest is calculated for both the principal and the interest generated, that is, the interest is favorable.
Compound interest calculation It is characterized by that the sum of principal and interest at the end of the previous period is taken as the principal of the next period, and the amount of principal of each period is different when calculating. Compound Calculation formula Yes: Present value It refers to the principal that must be invested today to reach a specific amount of funds in the future when compound interest is calculated. The so-called compound interest, also known as Li Shangli, refers to the method of making a new round of investment with capital and interest after a deposit or investment returns. Final value of compound interest It refers to the sum of the principal that adds the interest to the principal and recalculates the interest after the principal obtains the interest within the agreed period, and rolls over to the agreed period end. In short, it is the sum of the principal and interest after the initial deposit of A at the beginning of the period, with the interest rate of i as the interest rate. Formula: F=A * (1+i) ^ n For example: the principal is 50000 yuan, the interest rate or ROI 3%, and the investment period is 30 years Interest income , press Compound interest formula To calculate the sum of principal and interest（ final value ）Yes: 50000 × (1+3%) ^ 30 because, Inflation rate It is closely related to the interest rate, just like the positive and negative sides of a coin. Therefore, the formula for calculating the final value of compound interest can also be used to calculate the practical value 。 Just replace the interest rate in the formula with the inflation rate. principal.
For example, 30 years later, it will raise 3 million yuan old-age pension , assumed average year Rate of return If it is 3%, the principal that must be invested now is 3000000/(1+3%) ^ 30 Final value of compound interest
Commercial Press《 English Chinese Dictionary of Securities Investment 》Explanation: compound rate; compound interest ； interest on interest。 The interest generated jointly by the principal and the interest accrued in the previous interest period. That is, the new interest earned by the undrawn interest according to the interest rate of the principal, often called interest on interest and interest rolling interest, which not only generates interest on the principal, but also generates interest. Compound Calculation formula Yes: Where: P=principal; I=interest rate; n= Holding period Final value of ordinary annuity : refers to the sum of principal and interest of the equal amount of income or expenditure at the end of each period within a certain period, that is, the amount of each period is converted into the amount at the end of the last period by compound interest final value , and then add up to Final value of annuity 。 For example, the annual deposit is 1 yuan, Annual interest rate It is 10%. After five years, the annual final value and annuity final value are F=A [(1+i) ^ n-1]/i, which is recorded as F=A (F/A, i, n). The derivation is as follows:
Deposit at the end of one year: 1 yuan
Final value at the end of 2 years=1 * (1+10%)=(1+10%)
One yuan deposited at the end of two years
Final value at the end of 3 years=1 * (1+10%) ^ 2+1 * (1+10%)=(1+10%) ^ 2+(1+10%)
One yuan deposited at the end of three years
Final value at the end of 4 years=1 * (1+10%)^ 3+1 *(1+10%)^2+1*(1+10%)=(1+10%)^3+(1+10%)^2+(1+10%) One yuan deposited at the end of four years
Final value at the end of 5 years=1 * (1+10%) ^ 4+1 * (1+10%) ^ 3+1 * (1+10%) ^ 2+1 * (1+10%)=(1+10%) ^ 4+(1+10%) ^ 3+(1+10%) ^ 2+(1+10%)
Final value of one yuan annuity deposited at the end of 5 years F=(1+10%) ^ 4+(1+10%) ^ 3+(1+10%) ^ 2+(1+10%)+1
If there are many annuity periods, it is obviously quite cumbersome to calculate the final value with the above method. Since the annual payments are equal and the coefficient of converting the final value is regular, a simple calculation method can be found.
If the annual payment amount is A, the interest rate is i, and the number of periods is n, then Compound interest calculation The final annuity value F of is: F=A+A×(1+i)^1+…+A×(1+i)^(n-1)，
Sum Formula of Proportional Sequence
F=A[1-(1+i)^n]/[1-(1+i)]
F=A[1-(1+i)^n]/[1-1-i]
F=A [(1+i) ^ n-1]/iWhere [(1+i) ^ n-1]/i is normal Annuity terminal value coefficient , or the final value coefficient of the post paid annuity, the interest rate is i, and the final value of the annuity after n periods is recorded as (F/A，i,n), You can check the general annuity terminal value coefficient table. 
Compound interest
