Question

In how many years will (Kl 600) to (K 1852.20) at 5% per annum when compounded semiannually?

a) 6 years
b) 8 years
c) 10 years
d) 12 years

Answer 1

To calculate the number of years it will take for an amount to grow from (Kl 600) to (K 1852.20) at 5% per annum compounded semiannually, we can use the formula for compound interest. Plugging in the given values and solving for t, we find that it will take 8 years.

Step-by-step explanation:

To calculate the number of years it will take for an amount to grow from (Kl 600) to (K 1852.20) at 5% per annum compounded semiannually, we can use the formula for compound interest:

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

Where:

• A = Final amount
• P = Initial amount
• r = Annual interest rate
• n = Number of times interest is compounded per year
• t = Number of years

Plugging in the given values, we get:

(K 1852.20) = (Kl 600)(1 + 0.05/2)^(2t)

Simplifying the equation, we have:

1852.20/600 = (1 + 0.05/2)^(2t)

Taking the natural logarithm of both sides, we get:

ln(1852.20/600) = 2t * ln(1 + 0.05/2)

Now, we can solve for t by dividing both sides by 2 times the natural logarithm of (1 + 0.05/2). Finally, we obtain the value of t, which represents the number of years it will take.

The correct answer is b) 8 years.