To find out how much money to lend in order to earn Tshs. 48,000 in interest at a 6% annual interest rate over 6 months, we can use the formula for simple interest:
\[ I = P \times r \times t \]
where:
- \( I \) is the interest earned (Tshs. 48,000),
- \( P \) is the principal amount (the amount lent),
- \( r \) is the annual interest rate (6% or 0.06),
- \( t \) is the time period in years.
Since 6 months is half a year, we can convert it to years:
\[ t = \frac{6}{12} = 0.5 \text{ years} \]
Now substituting the known values into the formula:
\[ 48000 = P \times 0.06 \times 0.5 \]
Now, solve for \( P \):
\[ P = \frac{48000}{0.06 \times 0.5} \]
Calculating the denominator:
\[ 0.06 \times 0.5 = 0.03 \]
Now substituting that back into the equation for \( P \):
\[ P = \frac{48000}{0.03} = 1600000 \]
Therefore, you would need to lend Tshs. 1,600,000 to get Tshs. 48,000 in interest at a 6% interest rate over 6 months.
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