To calculate the future value of an investment with compound interest compounded weekly, you can use the formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the number of years the money is invested or borrowed.
Given:
- \(P = 1000\) birr
- \(r = 6% = 0.06\)
- \(n = 52\) (since interest is compounded weekly)
- \(t = 10\) years
Now plug in the values:
\[ A = 1000 \left(1 + \frac{0.06}{52}\right)^{52 \times 10} \]
Calculating inside the parentheses first:
\[ \frac{0.06}{52} = 0.00115384615 \]
Then add 1:
\[ 1 + 0.00115384615 = 1.00115384615 \]
Now calculate the exponent:
\[ 52 \times 10 = 520 \]
Now we calculate \(A\):
\[ A = 1000 \times (1.00115384615)^{520} \]
Calculating \((1.00115384615)^{520}\):
\[ (1.00115384615)^{520} \approx 1.7137 \text{ (using a calculator)} \]
Now, multiply by 1000:
\[ A \approx 1000 \times 1.7137 \approx 1713.70 \]
So, the future value of the investment of 1000 birr at 6% interest compounded weekly for 10 years is approximately 1713.70 birr.
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