Question

22. Calculate the present value of $5,000 received five years from today if your investments pay

 a. 6 percent compounded annually

 b. 8 percent compounded annually

 c. 10 percent compounded annually

 d. 10 percent compounded semiannually

 e. 10 percent compounded quarterly 

What do your answers to these questions tell you about the relation between present values and interest rates and between present values and the number of compounding periods per year? (LG 2-9) 

23. Calculate the future value in five years of $5,000 received today if your investments pay 

a. 6 percent compounded annually 

b. 8 percent compounded annually 

c. 10 percent compounded annually 

d. 10 percent compounded semiannually 

e. 10 percent compounded quarterlyWhat do your answers to these questions tell you about the relation between future values and interest rates and between future values and the number of compounding periods per year? (LG 2-9) 

Answer 1

Answer:

Given

Future value of Payment F=$5000

PV=FV/(1+r)^n

PV=Present value

r=interest rate

n= number of periods

for annual compounding

n=5

for semi annual compounding

n=2*5=10

for quarterly compounding

n=4*5=20

A)

For r=6% annual compounding

PV=5000/(1+6%)^5=$3736.29    EQ1

B)

For r=8% annual compounding

PV=5000/(1+8%)^5=$3402.92   EQ2

C)

For r=10% annual compounding

PV=5000/(1+10%)^5=$3104.61 EQ3

D)

For r=10% semi annual compounding

r=10%/2=5%

n=10

PV=5000/(1+5%)^10=$3069.57   EQ4

E)

For r=10% quarterly compounding

r=10%/4=2.5%

n=20

PV=5000/(1+2.5%)^20=$3051.35 EQ5

From equation 1 ,2 and 3 we find that as the interest rate increases , PV decreases. So there is inverse relationship between interest rate and PV.

From equation 3,4 and 5 we find that as the number of compounding increases , PV decreases. So there is inverse relationship between compounding and PV.

Answer 2

Given Future value of Payment F=$5000 or, PV=FV/(1+r)^n PV=Present value r=interest rate n= number of periods for annual compounding n=5 for semi annual compounding n=2*5=10 for quarterly compounding n=4*5=20 A) For r=6% annual compounding PV=5000/(1+6%)^5=$3736.29 B) For r=8% annual compounding PV=5000/(1+8%)^5=$3402.92 C) For r=10% annual compounding PV=5000/(1+10%)^5=$3104.61 D) For r=10% semi annual compounding r=10%/2=5% n=10 PV=5000/(1+5%)^10=$3069.57 E) For r=10% quarterly compounding r=10%/4=2.5% n=20 PV=5000/(1+2.5%)^20=$3051.35