an investment of $10,000.00 in the Emerging Country Debt fund in 2001 was worth 24,780 in 2006 money mag used the formual r=(s/p)^1/n -1 to find the 5 year average annual return. What is the return. How do I solve this

s = 24,780

p = 10,000

s/p = 2.478
(s/p)^(.2) = 1.199
subtract 1
.199
* 100 for percent --> 19.9%
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this comes from the compound interest formula for initial deposit p at interest rate r expressed as a decimal fraction for n years
amount in account = s = p * (1+r)^n
s/p = (1+r)^n
(s/p)^(1/n) = r+1

Thank you very much for your help I think in the past you have help me it made more scense after i read your post...If you could i have an earlier post that Candice replied to if you could look at it and let me know your thougts it would be great.

To calculate the 5-year average annual return using the given formula, you need to understand the variables:

r = Average annual return
s = Final value of the investment
p = Initial value of the investment
n = Number of years

In this case:
s = $24,780
p = $10,000
n = 5 (since it's a 5-year period)

Now, let's plug these values into the formula:

r = (s/p)^(1/n) - 1

r = (24,780/10,000)^(1/5) - 1

To solve this, let's break it down step by step:

Step 1: Calculate the value inside the parentheses
24,780/10,000 = 2.478

Step 2: Calculate the exponent
(1/5) = 0.2

Step 3: Calculate the value inside the parentheses again
2.478^0.2 = 1.0831

Step 4: Subtract 1 from the result
1.0831 - 1 = 0.0831

So, the return is approximately 0.0831 or 8.31%.

Therefore, the 5-year average annual return for the investment in the Emerging Country Debt fund is 8.31%.