Compound Interest

“Whenever interest is earn/paid on interested amount or on principle plus interest amount is called compound interest”

Year		Interest	Balance
1	100000*10%p.a	10000	110000
2	110000*10%p.a	11000	121000
3	121000*10%p.a	12100	133100
4	133100*10%p.a	13310	146410

Examples:

In banks loans or lease of assets e.t.c is the example of compound interest.

Formulas:

Future value = Present value (1+ rate of interest)^ no. of periods

Present value = Future value / (1+ rate of interest)^ no. of periods

Q # 1

The following are exercises in future (terminal) values:

At The end of three years, how much is an initial deposit of $ 100 worth, assuming a compound annual interest rate of 10 percent?

Solution a:

P.V = $100

r = 10 % p.a

n = 3 years

F.V = P.V(1+r)ⁿ

F.V= 100(1+0.10)³

F.V = 133.1

Q no 2 (Present value example)

The following are exercise in present value:

(a):$ 100 at the end of three year is worth how much today , assuming a discount rate of 10 %?

Solution:

We know that

P.V = F.V (1+r)^-n

P.V = 100 (1+0.10)^-3

P.V = 75

(b):What is the aggregate present value of $ 500 receive at the of each of the next three year, assuming a discount of 25 %?

Solution:

P.V = 500(1+0.25)^-3

P.V = 256

Question no 8:

Sales of the P.J. Cramer company were $ 500000 this year, and they are expected to grow at a compound rate of 20 % for next 6 years. What will be the sales figure at the  end of each of the next six year?  

Solution:

P.V = 500000

r = 20 %

 We will find the F.V at the end of each next six years

F.V = p(1+r)ⁿ

F.V year 1 = 500000(1+0.20) = $ 600000

F.V year 2 = 500000(1+0.20)²= $ 720000

F.V year 3 = 500000(1+0.20)³=$ 864000

F.V year 4 = 500000(1+0.20)⁴=$ 1036800

F.V year 5 = 500000(1+0.20)⁵=$1244160

F.V year 6 = 500000(1+0.20)⁶=$1492992