Chapter 4

If you receive $11,000 today and can invest it at a 6% annual rate, compounded continuously, what will be your ending value after 25 years?

$11,000(e)^rt =11,000e^(.06)25 =11,000e^1.5 =$49,298.58 In calc: 1.5=e =4.48....*11,000= 49,298.58

What is continuous compounding, and how do you find the future value of an amount that is continuously compounded?

CF0(e)^rt

You plan to make a series of deposits in an interest-bearing account. You will deposit $1,000 today, $2,000 in two years, and $8,000 in five years. If you withdraw $3,000 in three years and $5,000 in seven years, how much will you have after eight years if the interest rate is 9%?

CF0=1000 C01=0 C02=2000 C03= -3000 C04=0 C05=8000 C06=0 C07= -5000 CPT NPV I=9 NPV=2,831.0894=PV N=8 I/y=9 CPT FV = 5,641.12

Calculation of the effective annual rate (EAR); how does the frequency of compounding affect the EAR?

EAR = [1+r/t]^t - 1 More frequent compounding increases the EAR

The EAR for 12% compounded weekly is _____?

EAR=[1 + r/t]^t -1 [1+.12/52]^52 -1= 12.73%

Know the basic time value of money formula

FV=PV(1+r)^n

How does changing the discount rate and/or the number of periods affect the present value and/or future value?

Increasing r decreases PV and increases FV. Increasing n increases, PV increases

What does time value of money mean? How can a country have negative interest rates?

Money has a time value because you earn interest when you invest and you pay interest when you borrow

A retirement plan offers to pay $40,000 each year with the payments growing 4% per year for the next 25 years. The discount rate is 9%. What is the present value of this plan at retirement?

Use the growing annuity formula: PV=[C/(r-g)] [1-(1+g/1+r)^T] [40,000/(.09-.04)] [1-(1.04/1.09)^25] =800,000(1-.30915) =$552,680

For any given interest rate, the compound value of any given amount of money will be the smallest is compounding occurs _____?

Yearly