Question

Please demostrate!!

If you have $100,000 deposited with an interest rate of 6%. How much is your bank balance at the end of 1 year under the different frequency of compounding:

[1] annual compounding?

[2] semi-annual compounding?

[3] quarterly compounding?

[4] monthly compounding?

[5] daily compounding?

[6] continuous compounding?

Answer 1

a.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=100,000*(1.06)

=$106000

b.We use the formula:  
A=P(1+r/2)^2n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=100,000*(1+0.06/2)^(2*1)

=100,000*1.0609

=$106090

c.We use the formula:  
A=P(1+r/4)^4n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=100,000*(1+0.06/4)^(4*1)

=100,000*1.06136355

=$106136.36(Approx)

d.We use the formula:  
A=P(1+r/12)^12n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=100,000*(1+0.06/12)^(12*1)

=100,000*1.06167781

=$106167.78(Approx)

e.We use the formula:  
A=P(1+r/365)^365n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=100,000*(1+0.06/365)^(365*1)

=100,000*1.06183131

=$106183.13(Approx)

f.We use the formula:  
A=P(e)^rn
where   
A=future value
P=present value  
r=rate of interest
n=time period.

e=2.71828

A=100,000*(2.71828)^(0.06*1)

=100,000*1.0618365

=$106183.65(Approx)