# CLASS-9FINDING COMPOUND INTEREST WITH INCOMPLETE TIME PERIOD

Finding Compound Interest When Period Is Not a Complete Numbers Of Years -

Let it be 2 years 8 months. Then,

R                   8R/12

Amount = \$ { P ( 1 + ------ )²  X ( 1 + ------- )}

100                  100

Example.1) Calculate the amount and the compound interest on \$ 5000 for 3 years 6 months at 10% per annum, compound annually.

6          1

Ans.) Given, P = \$ 5000, R = 10% p.a, and Time = 3----- = 3----- years

12         2

As per the formula –

1

----- X R

R                      2

Amount = \$ { P ( 1 + --------- )ᶟ  X ( 1 + ---------- )}

100                      100

1

----- X 10

10                  2

Amount = \$ { 5000 ( 1 + ------ )ᶟ X ( 1 + ------------ )}

100                    100

1                    5

Amount = \$ { 5000 ( 1 + ------ )ᶟ  X ( 1 + ------- )}

10                   100

1                   5

Amount = \$ { 5000 ( 1 + ------ )ᶟ X ( 1 + ------ )}

10                 100

11                  1

Amount = \$ { 5000 ( ------ )ᶟ X ( 1 + ------ )}

10                 20

11 X 11 X 11           21

Amount = \$ ( 5000 X ---------------- X -------- )

10 X 10 X 10           20

5 X 1331 X 21              139755

Amount = \$ ( ---------------- ) = \$ ( ---------- ) = \$ 6987.75

20                        20

So, C.I = A – P =  \$ ( 6987.75 – 5000 ) = \$ 1987.75

Hence, amount = \$ 6987.75 and C.I = \$ 1987.75          (Ans.)