3.2 Calculation of Interest and Discounting 利息的计算与贴现

教学视频：

课堂练习：

问题讨论：

1. Simple Interest

Simple interest refers to the interest that earned only on the principal of the initial investment.

单利是指仅从初始投资本金上获得的利息。

expressed symbolically

Vn = V0(1 + i×n)

where Vn = the funds to be received by the lender at the end of year n ,note that this is a future value;

V0= the funds lent (and borrowed) now, note that this is a present value

2. Compound Interest
Compound interest involves earning interest on interest in addition to interest earned on the principal or initial investment.

复利是指在本金或初始投资的利息之外，再从利息中获得利息。

With annual compounding , the interest that accumulates during a year is added to the principal at year’s end, so that the following year your money earns interest on interest.

Vn = V0(1 + i)n

3 Discounting

Compounding is forward looking. Discounting is backward looking. It addresses this question: what is the present value of money to be received (or paid) in the future?

复利是向前看的。贴现是向后看的。它解决了这样一个问题:将来要收(或付)的钱的现值是多少?

The concept of present value is often used to compare returns or cost in daily economic life.

Example:

Suppose that you are about to buy a bond that will mature in one year，the face value is $1,000 and the coupon payment is $60 (the coupon rate 6%)

1)the prevailing market interest rate is 6%

How much will you be willing to pay

This is called at par.

2) When the interest rate rises

Suppose that the market interest rate rises to 8%

The price of the bond now becomes

You would be buying the bond for a price below its par value， (981.48<1,000)

this is called a discount from par, which raises the yield to maturity on the bond. 

3)When the interest rate falls

Suppose that the market interest rate falls to 4%

The price of the bond now becomes

You would be buying the bond for a price above its par value，(1,019.23>1,000) this is called a premium above par, which lowers the yield to maturity on the bond.

4)Conclusion

The price of a bond is the discounted value of the future stream of income over the life of the bond.

When the interest rate increases, the price of the bond decreases.

When the interest rate decreases, the price of the bonds increases.

Checkpoint:

Tom and Sally just had a baby. How much will they have to invest today for the baby to have $100,000 for college in 18 years if the interest rate is 5 percent? If the interest rate is 10 percent?