Question

Compounded weekly is investment of birr 1000 at 6% for 10 yeras?

Answer 1

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**.