Compound Interest Calculation

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: The final value (future value), or the value of the Benli, i.e. the end of the term.

P: Present value (Present value), or the opening amount.

A: An annuity (annuity), or an equal value.

I: Interest rate or discount rate

N: Number of interest periods

Compounding is characterized by the benli of the last term and the principal of the next period, in which the amount of principal is different in each period of the calculation. The formula for the principal and interest of compounding is: F=p (1+i) ^n

Compound interest is divided into discontinuous compounding and continuous compounding. On schedule (such as by year, half-year, quarter, month or day, etc.) the method of calculating compound interest is discontinuous compound interest; The method of compound interest is continuous compound interest by instantaneous calculation. In practical application, the method of discontinuous compound interest is generally used.

Folded Compounding Present Value

The present value of compound interest is the principal amount that must be invested in order to reach a particular fund in the future, in the case of compounding. The so-called compound interest is also referred to as the benefit of a deposit or investment after the return, and then even a new round of investment with the method.

Folded Compounding End Value

The final value of compounding refers to the sum of the principal amount of interest, which is accrued to the principal at the end of the contract period, after the principal has received interest within the agreed period.

Folded examples

For example: The principal is 50000 yuan, the interest rate or the return on investment is 3%, the investment life is 30, then 30 years after the principal + interest income, according to the compounding formula to calculate is: 50000x (1+3%) ^30

Because inflation is closely linked to interest rates, like the positive and negative sides of a coin, the formula for the end value of compounding can also be used to calculate the actual value of a particular fund in different years. Just change the rate in the formula to the rate of inflation.

For example, a pension of $3 million will be raised after 30, assuming an average annual return of 3%, then the principal amount to be invested is 3000000x1/(1+3%) ^30

The interest is settled once a year (settled at a single rate), and the principal and interest are then taken as the principal of the following year. This number is used as principal in the next year when interest is settled. There is more interest than the single interest rate.

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Mainly divided into 2 categories: one is to pay compound interest calculation: Benli and equal to the principal multiplied by (1+i) of the n-th square, the formula is F=p (1+i) ^n;

The other is equal to multiple payments compounding: Benli and equals principal multiplied by (1+i) n-squared-1 and then divided by interest I, the formula is F=a ((1+i) ^n-1)/I

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(1) Calculate the Benli final value of multiple equal investment

When each interest period starts with an equal amount of investment P, at the end of the N interest period, the final value is: Vc = px (1+i) x[(1+i) ^n-1]/i.

Obviously, when n=1, VC = px (1+i), that is, at the end of the first interest period, the final value only includes a one-time matching investment and interest, when n=2, VC = px (2+3xi+ixi), that is, at the end of the second interest period, The final value includes the first matching investment and its compound interest and the second time of the matching investment and its simple interest. In the construction project, the bidder needs multiple loans or the use of their own capital investment, the assumption that each time the amount of the same and the same interval, the project after the acceptance of the project section M, if the VC >m, the bidder is not suitable for bidding.

(2) Calculation of multiple equal value of the return

Assuming the same amount is collected each time and the interval is the same, the formula is: vc/n= px (1+i) ^nxi/[(1+i) ^n-1].

Obviously, when the n=1, v= px (1+i), that is, at the end of the first interest period, the total recovery of investment. In the construction project, the bidder once invested p, assuming that the tenderer at intervals to repay the winning bidder project funds M, if the vc/n>m, the bidder is not suitable for bidding.

Compound Interest Calculation