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Investing a SR 1,000 at 8% compounded semi annually Vs investing the same amount at 8%, the difference in interest gained is:

a- SR 160.00

b- SR 1.60

c- SR 0.16

d- SR 81.60

Answer :

The difference in interest gained between investing SR 1,000 at 8% compounded semiannually versus investing the same amount at 8% .We find that the difference in interest gained is SR 81.60, which corresponds to option d.

SR 81.60

The difference in interest gained between investing SR 1,000 at 8% compounded semiannually versus investing the same amount at 8% can be calculated using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the principal amount (SR 1,000 in this case)
r = the annual interest rate (8% or 0.08)
n = the number of times interest is compounded per year (2 for semiannual compounding)
t = the number of years

For the first scenario, where the interest is compounded semiannually, the calculation would be:

[tex]A1 = 1000(1 + 0.08/2)^(2*1)[/tex]For the second scenario, where the interest is not compounded, the calculation would be:

A2 = 1000(1 + 0.08*1)

Simplifying these calculations, we get:

[tex]A1 = 1000(1.04)^2A2 = 1000(1.08)[/tex]
Calculating the difference in interest gained:

Difference = A1 - A2

Substituting the values, we have:

[tex]Difference = 1000(1.04)^2 - 1000(1.08)[/tex]

Calculating this, we find that the difference in interest gained is SR 81.60, which corresponds to option d.

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