Calculate Interest Rate & Earnings: $150 -> $275 in 8yrs

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To calculate the interest rate needed for $150 to grow to $275 in 8 years with semi-annual compounding, the formula for compound interest can be applied. The interest rate can be derived from the equation A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. Additionally, for a $1000 deposit at 6% interest, the difference in earnings between semi-annual and annual compounding can be calculated using the same formula. The results will show how compounding frequency affects total returns. Understanding these calculations is essential for maximizing investment growth over time.
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1. Determine the interest rate for a principal of $150 to amount to $275 in 8 years with interest compounded semi-annually.

2. Suppose you deposit $1000 in an investment account for one year at 6%. How much more money will you receice if the investment is:
compounded semi-annually instead of annually.
 
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Use the equation

I = P( 1 + r/n ) ^nt
 
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