The rate of interest for first 2 years is 4%, for next 3 years is 5% and 8% for period beyond 5 years. If the Interest after 7 years is Rs.…

We know that, Simple Interest = (P × R × T)/100

Where, P = principal Amount, R = % Rate of interest, T = time period in years

Let the principle amount be Rs. x

? the interest rate is 4% per annum for first 2 years,

Simple Interest for first 2 years = (x × 4 × 2)/100 = 8x/100

? the interest rate is 5% per annum for next 3 years,

Simple Interest for next 3 years = (x × 5 × 3)/100 = 15x/100

Now, the time period remaining out of total time = 7 – (3 + 2) = 2 years

? the interest rate is 8% per annum for remaining 2 years,

Simple Interest for remaining 2 years = (x × 8 × 2)/100 = 16x/100

According to given information, total interest of 7 years = Rs. 780

∴ 780 = (8x/100) + (15x/100) + (16x/100)

⇒ 780 = 39x/100

⇒ x = (780 × 100)/39

⇒ x = 2000

∴ the principal amount is Rs. 2000.