Final answer:
To determine the time for $10,000 to yield $8,500 at 8.5% interest, we use the simple interest formula and find it requires 10 years. To then find the rate to double the sum in that time, we set the final amount to twice the principal and solve for the interest rate, yielding 10%. However, there is a discrepancy since the answer provided in the options is 'd) 8 years, 10%', which might suggest a potential error either in the calculation or the options given.
Step-by-step explanation:
To calculate the time needed for $10,000 to yield an interest of $8,500 at a rate of 8.5%, we use the formula for simple interest which is I = PRT, where I is the interest earned, P is the principal amount, R is the rate of interest, and T is the time in years. Plugging in the values, we get $8,500 = $10,000 × 0.085 × T, which simplifies to T equals 10 years.
To find the rate at which the principal will double in the same period, we use the equation for doubling at simple interest: Final Amount = Principal × (1 + RT). Since the final amount is twice the principal, we have $20,000 = $10,000 × (1 + R × 10), which simplifies to a rate R of 10%.
Therefore, the correct answer is 'd) 8 years, 10%', although there is a discrepancy as our calculation yielded 10 years for the doubling rate. It's important to note that this discrepancy needs to be addressed before any definitive conclusions are drawn.