Compound amount and interest

2. Compound Interest:
Interest computed on the original principal plus any
accrued
interest. Thus if 5% is the rate of interest per year and the
principal is Rs.1000, the compound amount after one year
will be Rs.1050, after two years it will be
Rs.1050 x 0.05 = Rs.1102.50,
After three years it will be
Rs.1102.50 x 0.05 = Rs.1157.63
After 3 years compound interest will be Rs. 157.63
and so forth mathematically, if p is the original
principal and r is the rate of interest expressed as a
decimal,
the compound amount at the end of the nth year will be
A = P (1 + r)n
Where
A= Compound amount OR future value OR Accumulated
value
P = Principal OR Present value
r = Rate of interest
n = Number of periods

3. Example-7
Find compound amount of Rs.6500 in 04 years at 6% per
annum and also find compound interest.
Solution:
P = Rs.6500
n = 4
r = 6% =
6
= 0.06
100
A=?
We know that
A = P (1 + r)n
A = 6500(1+0.06)4
A = Rs.8206.10
Where I = A- P = 8206.10-6500 = Rs.1706.1

4. Example-8
In what time compound amount on Rs.6500 is Rs.8206.10 at
6% per annum.
Solution:
P = Rs.6500
r = 6% =
6
= 0.06
100
A = 8206.10
n = ?
We know that
A = P (1 + r)n
8206.10=6500(1+0.06)n
n8206.10
= (1.06)
6500
Taking log to both sides
log
8206.10
= nlog(1.06)
6500
 
  
log8206.10 – log6500 = n×log(1.06)
3.9141-3.8129= n×(0.0253)
n
0.1012
0.0253
 = 04 years

5. Example-9
At what rate compound amount on Rs.6500 is Rs.8206.10 in
04 years.
Solution:
A= 8206.10
P = 6500
n = 04 years
r =?
We know that
A= P (1 + r)n
8206.10 = 6500(1+r)4
48206.10
= (1+r)
6500
1
4
(1.2625) = 1+r
1.0600 -1 = r
r = 0.0600 = 6%

6. Example-10
Find present value of compound amount Rs.8206.10 in 04 years
at 6% compounded.
Solution:
A= 8206.10
r = 6% =
6
= 0.06
100
n = 4
P = ?
We know that
A = P (1 + r)n
n 4
A 8206.10 8206.10
p = =
(1 r) (1 0.06) 1.262477

 
p Rs.6500