Answer :
Step-by-step explanation:
To determine which bank is a better option for Bindu to invest her money, let's analyze each option.
Option (a):
Principle amount (P) = 15000
Amount after 3 years (A) = 20175
The formula for compound interest is:
=
(
1
+
)
A=P(1+
n
r
)
nt
where:
P is the principal amount (initial investment),
r is the annual interest rate (as a decimal),
n is the number of times that interest is compounded per unit
t (years).
From option (a):
20175
=
15000
(
1
+
1
)
3
20175=15000(1+
1
r
)
3
Dividing both sides by 15000:
20175
15000
=
(
1
+
)
3
15000
20175
=(1+r)
3
1.345
=
(
1
+
)
3
1.345=(1+r)
3
Taking the cube root of both sides:
1
+
=
1.345
3
1+r=
3
1.345
1
+
≈
1.116
1+r≈1.116
≈
0.116
r≈0.116
So, the annual interest rate
r is approximately 11.6%.
Option (b):
Principle amount (P) = 24000
Amount after 4 years (A) = 34720
From option (b):
34720
=
24000
(
1
+
1
)
4
34720=24000(1+
1
r
)
4
Dividing both sides by 24000:
34720
24000
=
(
1
+
)
4
24000
34720
=(1+r)
4
1.44733
=
(
1
+
)
4
1.44733=(1+r)
4
Taking the fourth root of both sides:
1
+
=
1.44733
4
1+r=
4
1.44733
1
+
≈
1.122
1+r≈1.122
≈
0.122
r≈0.122
So, the annual interest rate
r is approximately 12.2%.
Conclusion:
Option (a) offers an annual interest rate of approximately 11.6%.
Option (b) offers an annual interest rate of approximately 12.2%.
Therefore, option (b) is the better option for Bindu to invest her money, as it offers a higher annual interest rate compared to option (a)