1.

If a certain sum of money is compounded annually at the rate of 15% per annum, find the ratio of amount due in 7th year to the 8th year.1). 17 : 192). 20 : 233). 20 : 214). 23 : 27

Answer»

We know that:

Amount:

$(A = \LEFT[ {P{{\left( {1 + \frac{r}{{100}}} \right)}^t}} \right])$ 

Where, A = amount INCLUDING interest

P = principal

r = rate of interest

t = time period

Now, ACCORDING to the question,

Amount after 7th year-

$(= P{\left( {1 + \frac{{15}}{{100}}} \right)^7})$ 

Amount after 8th year-

$(= P{\left( {1 + \frac{{15}}{{100}}} \right)^8} = P\left[ {{{\left( {1 + \frac{{15}}{{100}}} \right)}^7} \times {{\left( {1 + \frac{{15}}{{100}}} \right)}^1}} \right])$ 

∴ required ratio-

$(= \frac{{P{{\left( {1 + \frac{{15}}{{100}}} \right)}^7}}}{{P\left[ {{{\left( {1 + \frac{{15}}{{100}}} \right)}^7} \times {{\left( {1 + \frac{{15}}{{100}}} \right)}^1}} \right]}} = \frac{1}{{1 + \frac{{15}}{{100}}}} = \frac{{100}}{{115}} = \frac{{20}}{{23}} = 20:23)$ 

HENCE, the required ratio is 20 : 23.


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