Correct Answer - Option 1 : Rs. 1000
Given:
Simple Interest = Rs. 770
Rate = 4% for 3 years
Rate = 5% for 3 years to 8 years
Rate = 8% for beyond 8 years
Time = 13 years
Formula used:
S.I = (P × R × T)/100
Where:
S.I = Simple Interest
P = Principal, R = Rate, T = Time
Calculation:
Let the principal amount be Rs. P
The interest rate is 4% per annum for first 3 years,
Simple Interest for first 3 years = (P × 4 × 3)/100 = (12/100)P
The interest rate is 5% per annum for next 5 years,
Simple Interest for next 5 years = (P × 5 × 5)/100 = (25/100)P
Now, the time period remaining out of total time = 13 – (5 + 3) = 5 years
The interest rate is 8% per annum for remaining 5 years,
Simple Interest for remaining 5 years = (P × 8 × 5)/100 = (40/100)P
According to given information, we have
Total interest of 13 years = Rs. 770
770 = (12/100)P + (25/100)P + (40/100)P
⇒ 770 = {(12/100) + (25/100) + (40/100)}P
⇒ 770 = (77/100)P
⇒ P = (770 × 100)/77
⇒ P = 1000
∴ The principal amount is Rs. 1000.