Question

A certain sum of money amounts to $12,100 in 2 years and $13,310 in 3 years at a certain rate. Find the rate and the sum.

a) Rate: $605 per year, Sum: $10,000
b) Rate: $605 per year, Sum: $11,000
c) Rate: $605 per year, Sum: $12,100
d) Rate: $10,000 per year, Sum: $605

Answer 1

Calculations using the simple interest formula have shown a discrepancy, as $1,210 is the interest for one year, leading to a deduction that the principal would be $9,680, which doesn't match any of the provided options.

Step-by-step explanation:

When solving for the interest rate and the principal sum of money, we utilize the formula for simple interest: Interest = Principal × rate × time. In the given problem, we know that the amount after 2 years is $12,100 and after 3 years is $13,310. The difference between these two amounts is due to one year's interest, which can be calculated as $13,310 - $12,100 = $1,210.

The yearly interest rate is the same each year, so we now know that $1,210 is the interest for one year. Therefore, the interest for two years is $1,210 × 2 = $2,420. Using this, we can find the principal by subtracting the total interest from the amount after 2 years: $12,100 - $2,420 = $9,680. However, this is not an option among the answers provided.

Since there might be a mistake in the process or provided options, we should re-check the calculation. If no mistake is found, we should inform the student about the discrepancy and guide them to consult further with their teacher or reference materials for the correct figures.