What Is the Time Value of Money?

The time value of money refers to the value added by the investment and reinvestment of money over a certain period of time, also known as the time value of funds.

Time value of money

Benjamin Frank said:

Definition of the time value of money : From the perspective of quantity, the time value of money is no risk and no

1.Calculation of simple interest

The principal earns interest during the term of the loan, and no matter how long the interest is generated, the principal is not added to the principal and the interest is calculated twice.

Time value of money

P principal, also known as opening amount or present value;

I -interest;

i -interest rate, usually the ratio of annual interest to principal;

F -the sum of principal and interest, also known as the principal and interest or the final value;

t (n)-time (number of periods in which interest is calculated).

Simple interest calculation:

I = P * i * t

Example: An enterprise has an interest-bearing promissory note with a face value of 1200 yuan and a coupon rate of 4%. The date of ticket is June 15 and August 14 expires (a total of 60 days).

For: I = 1200 × 4% × 60/360 = 8 yuan

Final value calculation: F = P + P × i × t

Present value calculation: P = F / (1 + i * t)

2. Compound interest calculation

After each interest accrual period, the interest generated is added to the principal and interest is calculated again, which is calculated on a period-by-period basis, commonly known as "profit rolling".

(1) Final value of compound interest

F = P (1 + i) ^ n

Among them, (1 + i) ^ n is called the compound final value coefficient or the compound final value of 1 yuan, which is represented by the symbol (F / P, i, n).

(2) Present value of compound interest

P = F (1 + i) ^-n

Among them, (1 + i) ^ n is called the compound interest present value coefficient, or the compound present value of 1 yuan, which is expressed by (P / F, i, n).

Time value of money

(3) Compound interest

I = SP

The final value of a 1 yuan investment with an annual interest rate of 8% over different time periods

Time value of money

(4) Nominal interest rate and real interest rate

The interest rate of compound interest may not always be one year, it may be quarter, month, or day. When interest is compounded several times a year, the annual interest rate given is called the nominal interest rate.

Example: The principal is 1,000 yuan, the investment is 5 years, and the interest rate is 8%.

F = 1000 × (1 + 8%) ^ 5 = 1000 × 1.469 = 1469

I = 1469--1000 = 469

If you compound interest every quarter,

Quarterly interest rate = 8% / 4 = 2%

Compound interest times = 5 × 4 = 20

F = 1000 × (1 + 2%) ^ 20 = 1000 × 1.486 = 1486

I = 1486 & shy; 1000 = 486

When compounding interest several times a year, the actual interest received is higher than the interest calculated at the nominal interest rate.

Real interest rate

F = P * (1 + i) ^ n

1486 = 1000 × (1 + i) ^ 5