Final answer:
To find the total value of a $5,000 investment at 3% simple interest over 15 years, one needs to use the formula Total Future Amount = Principal + (Principal × Rate × Time). The correct simple interest would be $150 annually, not $15, resulting in a total future amount of $7,250 which does not match any of the provided options, indicating a potential error in the question.
Step-by-step explanation:
The question asks for the total value of a $5,000 investment earning 3% interest for 15 years. When calculating the future value of this investment, compound interest is typically used, but given the information that the simple interest is $15, this implies each year 3% of $5,000 is accumulated as interest. However, there seems to be a mistake here, because 3% of $5,000 would actually be $150, not $15. Assuming we use the corrected simple interest amount, the simple formula for future value with simple interest is:
Total Future Amount = Principal + (Principal × Rate × Time)
For this calculation:
- Principal = $5,000
- Rate (in decimal) = 0.03
- Time = 15 years
Let's calculate:
Total Future Amount = $5,000 + ($5,000 × 0.03 × 15) = $5,000 + ($5,000 × 0.45) = $5,000 + $2,250 = $7,250
Since $7,250 is not one of the options, the question seems to contain an error either in the presented interest calculation or the options provided. If compounding annually, we would use a different formula:
Total Future Amount = Principal × (1 + Rate)ⁿ
In that case, the total future amount would be higher, but without the correct options or accurate information on the compounding frequency, we cannot provide an exact answer from the given options.