# The rate of interest for the first 3 years is 4%, for the next 5 years is 5%, and 8% for the period beyond 8 years. If the Interest after 13 years is

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The rate of interest for the first 3 years is 4%, for the next 5 years is 5%, and 8% for the period beyond 8 years. If the Interest after 13 years is Rs. 770. Find the principle (in Rs.)

1. Rs. 1000
2. Rs. 2000
3. Rs. 3000
4. Rs. 4000

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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.