If $100,000 is invested at an annual interest rate of 6%, how much more will the investment be worth at the end of the first year if the interest is compounded at the end of 6 months and again at the end of the year instead of just at the end of the year?
At least $10, but less than $100.
When $100,000 is invested at an annual interest rate of 6%, compounding the interest semi-annually results in a higher total than compounding it just once at the end of the year. Specifically, the additional interest earned due to more frequent compounding will be between $10 and $100.
The difference in interest earned from semi-annual compounding compared to annual compounding is greater than $10. This option underestimates the effect of compounding frequency on the total interest accrued over the year.
This option accurately reflects the additional interest earned. When compounded semi-annually, the investment grows to approximately $106,000, resulting in an extra $10,000 in interest earned compared to annual compounding, which yields $106,000 as well. The additional interest falls within the range of $10 to $100.
This option overestimates the additional interest earned from semi-annual compounding. The actual increase from compounding more frequently is not substantial enough to reach the $100 mark, thus making this choice incorrect.
This choice greatly exaggerates the impact of compounding frequency. The difference in interest between semi-annual and annual compounding is far less than $1,000, making this option implausible.
This option is incorrect as it suggests an unrealistically high additional interest amount. The actual increase is significantly lower than $10,000, which makes this choice incorrect.
Compounding interest more frequently increases the total amount of interest earned on an investment. For a $100,000 investment at a 6% annual rate, compounding interest semi-annually yields an additional interest amount that falls between $10 and $100. Thus, understanding the effects of compounding frequency is essential for maximizing investment returns.
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