CHAPTER 4 Part ….3

The Time Value of Money

Created By

Eng. Maysa Faroon Gharaybeh

Quiz:

• Chapter4 (part2 + part3)

• 55, 60, 62, 68, 72, 95, 99, 100, 103, 112, 113, 115, 116.

Interest Rates That Vary With Time

• Find the present equivalent value given a future value and a varying interest rate over the period of the loan ik : the interest rate of the kth period

• FN P = ----------------- eq.(4-31)

N (1 + ik)

• (P/F,i%,N)= 1/(1+i)N eq.(4-2)

k + 1

You can use (F/P,i%,N)= (1+i)N

Example:

If F4 = $1,000 and i1 = 10% , i2 = 12%, i3= 13% and i4=10% then

P = $1,000* (P/F, 10%, 1)* (P/F, 12%, 1)* (P/F, 13%, 1)* (P/F, 10%, 1)

P = $1,000 (0.9091)(0.8929)(0.8850)(0.9091)

Nominal And Effective Interest Rates

• Nominal Interest Rate (r ) For rates compounded more frequently than one time a year, the stated annual interest rate.

• Effective Interest Rate ( i ) For rates compounded more frequently than one year, the actual amount of interest paid.

• i = ( 1 + r / M )M - 1 M : the number of compounding periods per year

• Annual Percentage Rate ( APR ) percentage rate per period times number of periods. APR = (r/M) x M

Method1

Method2

This kind of problems can be solved with two ways :

1. get the effective interest rate which is compatible with the period for

example i = 16.14 per year compounded yearly and N = 10 years

OR

2. use the effective interest rate per quarter = 6%(nominal per year) / 4

(compounded times per year) = 1.5% per quarter compounded quarterly

and N = 10 years * 4 = 40 quarter periods

Continuous Compounding and Discrete Cash Flows

• Continuous compounding assumes cash flows occur at discrete intervals, but compounding is continuous throughout the interval.

• Given nominal per year interest rate r, compounding per year M one unit of principal = [ 1 + (r / M ) ] M

• Given M / r = p, [ 1 + (r / M ) ] M = [1 + (1/p) ] rp

• Given lim (p ∞ ) = [ 1 + (1 / p) ] rp = er

• ( F / P, r%, N ) = (1+i)N = e rN

Then i = e r - 1

• End of Chapter 4 PART 3

• See you next lecture with a very important revision !!!

• Don’t, miss it !!!!!