What annually compounded rate per year will give the same value at the end of 12 years as 10% p.a. simple interest? (State your answer in percentage terms and round to 2 decimal places, e.g. put 4.59 if your answer is 0.04586384)

To find the annually compounded rate that will give the same value at the end of 12 years as 10% p.a. simple interest, we need to equate the future value (FV) of an investment under simple interest and compound interest.

The formula for the future value with simple interest is:

FV_simple = P * (1 + r_simple * t)

Where: P = Principal amount (we can assume this to be $1 for simplicity) r_simple = Simple interest rate (10% p.a. = 0.10) t = Time period in years (12 years)

FV_simple = 1 * (1 + 0.10 * 12) FV_simple = 1 * (1 + 1.20) FV_simple = $2.20

The formula for the future value with compound interest is:

FV_compound = P * (1 + r_compound)^t

Where: r_compound = Compound interest rate (this is what we're trying to find)

We can set FV_simple equal to FV_compound and solve for r_compound:

2.20 = 1 * (1 + r_compound)^12 2.20 = (1 + r_compound)^12 Take the 12th root of both sides: 1.064 = 1 + r_compound Subtract 1 from both sides: r_compound = 0.064 or 6.4%

Therefore, an annually compounded rate of approximately 6.4% per year will give the same value at the end of 12 years as 10% p.a. simple interest.