Answer:
The interest earned by Sarah would be approximately sh. -1,158,336.50. Note that this is a negative value because Sarah has not earned interest; instead, she has paid sh. 1,158,336.50 more than her initial investment due to the interest on the scheme.
Explanation:
To determine the interest Sarah would earn on her investments, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (the initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, Sarah invests sh. 500,000 at the end of each year for four years, and the interest is compounded semi-annually. So:
P = sh. 500,000 (the amount invested at the end of each year)
r = 13% per year, or 0.13 as a decimal
n = 2 (semi-annual compounding means twice a year)
t = 4 years (the investment is made for four years)
Now, plug these values into the formula:
A = sh. 500,000 * (1 + 0.13/2)^(2*4)
First, calculate the values inside the parentheses:
1 + 0.13/2 = 1.065
Now, calculate the exponent:
2 * 4 = 8
Now, substitute these values back into the formula and calculate:
A = sh. 500,000 * (1.065)^8
A ≈ sh. 500,000 * 1.683327
A ≈ sh. 841,663.50
Now, to find the interest earned, subtract the principal amount (the total amount invested) from the future value:
Interest = A - Total Investment
Interest = sh. 841,663.50 - (sh. 500,000 * 4)
Interest = sh. 841,663.50 - sh. 2,000,000
Interest = sh. -1,158,336.50
The interest earned by Sarah would be approximately sh. -1,158,336.50. Note that this is a negative value because Sarah has not earned interest; instead, she has paid sh. 1,158,336.50 more than her initial investment due to the interest on the scheme.