Let’s now assume that your ancestor invested the $1,000 dollars in a bank account earning 6.8% simple interest per year for the 200-year period. How much money would be in the bank account?

Question

BlackTom AI · Accepted Answer

We start by restating the scenario and the given values to anchor our calculations: an initial principal of $1,000 is invested at a simple interest rate of 6.8% per year for 200 years.

First, compute the total simple interest earned using the formula I = P × r × t, where P = 1000, r = 0.068, and t = 200. Multiplying these together: 1000 × 0.068 = 68; then 68 × 200 = 13,600. This is the amount of interest earned over the 200 years.

Next, find the final account balance by adding the interest to the principal: Final amount = Principal + Interest = 1000 + 13,600 = 14,600.

Now evaluate each answer choice:
- Option a: $14,940. This would imply a total interest of $13,940, which corresponds to a higher effective rate or a compounding scenario, not the simple interest case given. Since the problem specifies simple interest, this is inconsistent with I = P × r × t and the numbers provided.
- Option b: $14,600. This matches the calculation exactly: 1,000 initial plus 13,600 interest equals 14,600. It aligns with the simple interest formula for 200 years at 6.8% on $1,000.
- Option c: $14,490. This is $110 more than the principal, which would correspond to an interest of $14,490 − $1,000 = $13,490. That would require a slightly smaller product of r × t, which does not fit the given rate and time.
- Option d: $15,700. This would imply $14,700 in interest, which again does not match the computed I = 13,600 under simple interest; it suggests either a higher rate, longer time, or compounding not described in the problem.
- Option e: $15,400. Here, the interest would be $14,400, which is larger than the correct $13,600, indicating an overestimation relative to the stated rate and period.

In this kind of question, the key source of confusion often lies in whether interest is simple or compounded, and in correctly applying the formula I = P × r × t for simple interest. Since the problem explicitly states simple interest and provides the principal, rate, and time, the correct final balance is found by adding the calculated interest to the principal only once, with no compounding effects within the period.

Summarizing the reasoning for each option helps distinguish the correct path from common missteps: the incorrect choices tend to assume additional interest accumulation beyond simple interest, misapply the rate, or mistakenly treat the period or the base as different, leading to totals that deviate from 14,600.

Let’s now assume that your ancestor invested the $1,000 dollars in a bank account earning 6.8% simple interest per year for the 200-year period. How much money would be in the bank account?单项选择题

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