What will be the amount (in ₹) of a sum of ₹6,000 in 2
4
1
years at 13
3
1
% p.a. if the interest is compounded 9-monthly?
- A7,986
- B8,429
- C7,869
- D7,896
Solution & Step-by-step Explanation
Given:
Principal (P) = ₹6,000
Time (T) = 2
4
1
years=2.25 years=2.25×12=27 months
Rate (R) = 13
3
1
% p.a.=
3
40
% p.a.
Since the interest is compounded 9-monthly:
Number of compounding cycles (n) =
9 months
27 months
=3 cycles
Rate per compounding cycle (R
′
) =
3
40
%×
12
9
=
3
40
×
4
3
=10% per cycle
Now, use the compound interest formula for the amount (A):
A=P(1+
100
R
′
)
n
A=6000(1+
100
10
)
3
A=6000×(1.1)
3
A=6000×1.331=7986
Thus, the total amount is ₹7,986.
Principal (P) = ₹6,000
Time (T) = 2
4
1
years=2.25 years=2.25×12=27 months
Rate (R) = 13
3
1
% p.a.=
3
40
% p.a.
Since the interest is compounded 9-monthly:
Number of compounding cycles (n) =
9 months
27 months
=3 cycles
Rate per compounding cycle (R
′
) =
3
40
%×
12
9
=
3
40
×
4
3
=10% per cycle
Now, use the compound interest formula for the amount (A):
A=P(1+
100
R
′
)
n
A=6000(1+
100
10
)
3
A=6000×(1.1)
3
A=6000×1.331=7986
Thus, the total amount is ₹7,986.