Question

In how many months will rs 8,000 yield rs 2,648 as compound interest at 20% per annum compounded semi-annually? (a) 18 (c) 12 (b) 24

Answer 1

Answer:

(a) 18

Explanation:

Amount is given as the sum of Principal and the compound interest;

$Amount= 8000+2648\\Amount=10648$

The compound interest of 20% is effective p.a. However, it can be converted to be effective per half-year.

$1+i=(1+\frac{i^{(p)} }{p})^p$

This can be rearranged as follows;

$i^{(p)}=P*[(1+i)^{\frac{1}{p} }-1]$

In our case P=2, i=20%=0.2

Therefore;

$\frac{i^{(2)}}{2} =[(1+0.2)^{0.5}-1] \\\frac{i^{(2)}}{2}=0.095445$

Therefore the compound interest effective semi-annually is 9.5445%

Consequently, the number of periods doubles.

Therefore

$10648=8000(1+0.095445)^{2t}1.331=1.095445^{2t}$

taking natural logarithms on both sides;

$ln 1.331=ln1.095445^{2t}$

applying laws of logarithms we get

$ln 1.331=2t*ln1.095445\\2t=\frac{ln 1.331}{ln1.095445} \\2t=3.136556\\t=1.5683 years$

This period converted to months is

$1.568*12=18.8 months$ approximately

Therefore the first choice is correct

Answer 2

Answer:

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