Shortcut Trick
The multiplying factor for a 5% increase is 1.05.
Total amount = (Investment 1 compounded for 2 years) + (Investment 2 compounded for 1 year)
Total amount = 100 × (1.05)2 + 100 × 1.05
Total amount = (100 × 1.1025) + 105 = 110.25 + 105 = 215.25
∴ The correct answer is Rs. 215.25.
Alternate Method
Given:
Investment at the start of each year (P) = Rs. 100
Rate of Interest (R) = 5% per annum
Formula Used:
Compound Amount (A) = P × (1 + R ÷ 100)n
Start Year 1
Start Year 2
End Year 2
Rs. 100
2 years @ 5% CI
Rs. 110.25
Rs. 100
1 year @ 5% CI
Rs. 105.00
Total: Rs. 215.25
Calculations:
⇒ Amount of 1st investment (n = 2) = 100 × (1 + 5 ÷ 100)2
⇒ Amount of 1st investment = 100 × (1.05)2
⇒ Amount of 1st investment = 100 × 1.1025 = 110.25
⇒ Amount of 2nd investment (n = 1) = 100 × (1 + 5 ÷ 100)1
⇒ Amount of 2nd investment = 100 × 1.05 = 105
⇒ Total Amount at the end of the 2nd year = 110.25 + 105
⇒ Total Amount = 215.25
∴ The correct answer is Rs. 215.25.
Additional Information
Effective Rate of Compound Interest
For 2 years at R% per annum, the effective compound interest rate can be calculated directly as 2R + (R2) ÷ 100 %.
Difference Between CI and SI
The exact numerical difference between Compound Interest and Simple Interest over a period of 2 years on a principal P is given by D = P × (R ÷ 100)2.
Simple Interest vs Compound Interest
Simple Interest is calculated only on the initial principal (SI = P × R × T ÷ 100), whereas Compound Interest accumulates on both the principal and the interest previously added.