At what rate percent p.a will a sum of Rs. 4000 amount to Rs. 5290 in 2 years when compounded annually?
step by step
Answers
Answer:
amount= p(1+R/100)²
5290=4000(1+R/100)²
1+R/100=√529/400
R/100=23/20-1
R/100=3/20
R=15%
The rate of compound interest is 15%.
Step-by-step explanation:
Given : If Rs 4000 amounts to Rs 5290 in 2 years .
To find : The rate of compound interest.
Solution :
Using compound interest formula,
A=P(1+r)^tA=P(1+r)
t
P is the principle P=Rs.4000
r is the rate
t is the time t= 2 years
Substitute the value,
A=P(1+\frac{r}{100})^tA=P(1+
100
r
)
t
5290=(4000)(1+\frac{r}{100})^25290=(4000)(1+
100
r
)
2
\frac{5290}{4000}=(1+\frac{r}{100})^2
4000
5290
=(1+
100
r
)
2
1.3225=(1+\frac{r}{100})^21.3225=(1+
100
r
)
2
Taking root both side,
\sqrt{1.3225}=1+\frac{r}{100}
1.3225
=1+
100
r
1.15=1+\frac{r}{100}1.15=1+
100
r
\frac{r}{100}=0.15
100
r
=0.15
r=15\%r=15%
Therefore, The rate of compound interest is 15%.
Hope it helps