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Sarah invests sh. 500,000 at the end of every year for four years in a scheme that pays 13% interest per year compounded semi -annually. 1. Determine the interest that she would earn

User Yaya
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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.

User Remko Jansen
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