A = P + (P * r * t),
where A is the total amount after time t, P is the principal amount, r is the rate of interest per annum, and t is the time in years.
From the problem, we know that after 2 years, the amount is 34,800. This gives us the first equation: 34,800 = P + (P * r * 2).
After 5 years, the amount is 42,000, giving us the second equation: 42,000 = P + (P * r * 5).
Next, we can rearrange these equations. From the first equation, we have: 34,800 = P(1 + 2r).
From the second equation, we have: 42,000 = P(1 + 5r).
Now, we divide the second equation by the first equation: (42,000 / 34,800) = (P(1 + 5r) / P(1 + 2r)).
This simplifies to: (42,000 / 34,800) = (1 + 5r) / (1 + 2r).
Calculating the left side, we get approximately 1.2069.
Cross-multiplying gives: 42,000(1 + 2r) = 34,800(1 + 5r).
Expanding both sides results in: 42,000 + 84,000r = 34,800 + 174,000r.
Rearranging this gives: 42,000 - 34,800 = 174,000r - 84,000r.
This simplifies to: 7,200 = 90,000r.
Thus, r = 7,200 / 90,000, which simplifies to 0.08 or 8%.
Next, we find the principal amount by substituting r = 0.08 back into the first equation: 34,800 = P(1 + 2 * 0.08), which gives: 34,800 = P(1 + 0.16) = P(1.16).
This means P = 34,800 / 1.16, which equals approximately 30,000.
Therefore, the rate of interest is 8%, and the principal sum is 30,000. The correct answer is 3. 8%, 30,000.
Year-wise PYQs
