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.)