Question

1)“For each of the following questions, determine the future value of the given principals when compounded (a) annually, (b) semiannually, (c) quarterly, and (d) continuously. 1 a)$1000 at 8 percent for 5 years.

b)“$10,000 at 9 percent for 8 years.”

2)“Determine the present value of $5000 to be paid in 8 years time if current interest of 10 percent is compounded (a) annually, (b) semiannually, (c) quarterly, and (d) continuously.”

Answer 1

Solution

1. Future value=Principal*(1+r)^n

Where

r= interest per period

n= number of periods

a. For annual compounding @ 8% for 5 years

FV= Principal*(1+r)^n

=1000*(1+.08)^5

=1469.328

b. For semi annual compounding @ 8% for 5 years

r=8/2=4%

n=5*2=10

FV=1000*(1+.04)^10

=1480.244

c. For quaterly compounding

r=8/4=2%

n=5*4=20

FV=1000*(1+.02)^20

=1485.947

d. For continuos compounding

FV=Principal*exp^r*t

FV=1000*exp^.08*5

=1491.825

For $10,000 at 9 percent for 8 years.”

a. For annual compounding @ 9% for 8 years

FV= Principal*(1+r)^n

=10000*(1+.09)^8

=19925.626

b. For semi annual compounding @ 9% for 8years

r=9/2=4.5%

n=8*2=16

FV=10000*(1+.045)^16

=20223.702

c. For quaterly compounding

r=9/4=2.25%

n=8*4=32

FV=10000*(1+.0225)^32

=20381.030

d. For continuos compounding

FV=Principal*exp^r*t

FV=10000*exp^.09*8

=20544.332