A person invest Rs.10000 for 2 years at a certain rate of interest compounded annually. at the end of 1 year this sum amounts to 11200. calculate
1) the rate of interest per annum
2) the amount at the end of second year
Answers
solution
sum amount at last of first year
principal+ principal× rate/100
= 10000+10000×rate/100
10000+100×rate= 11200 ( given)
100×rate= 1200 or rate= 1200/100= 12
(1) rate= 12% per annum
again
amount. at the end of 2nd year
11200+11200×12/100
= 11200 + 1344
= 12544
(2) amount at the end of second year
= 12544
Rate of interest = 12 % annually and
total sum = 12544 Rs
Step-by-step explanation:
Given,
principal amount, P = 10000
Time, t = 2 years
At the end of one year the sum is, A = 11200
According to the formula of compound interest,
A = P(1+ n ) nt
where, A = total sum
P = principal amount
t = time in years
r = interest rate
=>\ 11200\ =\ 10000(1+r)^1=> 11200 = 10000(1+r)
1
=>\ \dfrac{11200}{10000}\ =\ 1+r=>
10000
11200 = 1+r
=> r = 0.12
Hence, rate of interest in 12% annually.
For t = 2 years
A = P(1+\dfrac{r}{n})^{nt}A = P(1+nr ) nt
=\ 10000(1+0.12)^2 = 10000(1+0.12) 2
= 12544
Hence, the total sum after the end of 2 years is 12544 Rs.