Rs. 4,300 becomes Rs. 4644 in 2 years at simple interest. Find the principal amount that will become Rs. 10,104 in 5 years at the same rate of interest.
Options are:-
a) Rs. 7200
b) Rs. 9260
c) Rs. 8420
d) Rs. 5710
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Answer:
- The principal amount that will become c) Rs. 8420.
Step-by-step explanation:
Given that:
- Rs. 4,300 becomes Rs. 4,644 in 2 years at simple interest.
To Find:
- The principal amount that will become Rs. 10,104 in 5 years at the same rate of interest.
Formula used:
- S.I. = A - P = (P × R × T)/100
Where,
- S.I. = Simple interest
- A = Amount = Rs. 4,644
- P = Principal = Rs. 4,300
- R = Rate
- T = Time = 2 years
Finding the rate of interest:
S.I. = 4644 - 4300 = (4300 × R × 2)/100
⟶ 344 = 8600R/100
⟶ 344 = 86R
⟶ R = 344/86
⟶ R = 4
∴ Rate of interest = 4% p.a.
Now we have:
- Let Principal be P.
- A = Amount = Rs. 10,104
- R = Rate = 4% p.a.
- T = Time = 5 years
Finding the principal amount:
S.I. = 10104 - P = (P × 4 × 5)/100
⟶ 10104 - P = 20P/100
⟶ 10104 - P = 2P/10
⟶ 10(10104 - P) = 2P
⟶ 101040 - 10P = 2P
⟶ 101040 = 2P + 10P
⟶ 101040 = 12P
⟶ P = 101040/12
⟶ P = 8420
∴ Principal amount = Rs 8,420
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