You invest $10,000 in Rapid Growth Funds, which appreciate by 3% per year, with yields reinvested quarterly. By how much will your investment have grown after 8 years?

To calculate how much your investment will have grown after 8 years with a 3% annual appreciation rate and quarterly reinvestment of yields, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment
P = the principal investment amount ($10,000)
r = the annual interest rate (3% or 0.03)
n = the number of times interest is compounded per year (quarterly, so 4 times)
t = the number of years (8 years)

Now let's substitute these values into the formula:

A = 10000(1 + 0.03/4)^(4 * 8)

To simplify the calculation, let's solve this step-by-step:

1. Divide the annual interest rate (0.03) by the number of times it is compounded per year (4):
r/n = 0.03/4 = 0.0075

2. Add 1 to this result:
1 + r/n = 1 + 0.0075 = 1.0075

3. Multiply the number of times the interest is compounded per year (4) by the number of years (8):
nt = 4 * 8 = 32

4. Raise the previous result (1.0075) to the power of (32):
(1.0075)^32 = 1.265414784

5. Multiply the principal investment amount ($10,000) by the result from step 4:
A = 10000 * 1.265414784 = $12,654.15 (rounded to two decimal places)

Therefore, your investment will have grown to approximately $12,654.15 after 8 years with the given parameters.

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