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Examples 5 to 8

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(5) If the compound interest on a certain sum for 3 years at 10 % per annum be Rs. 49.65, what would be the sum ?

Soln. We always know that, the C.I. for Rs. 1000 for 3 years at 10 % p.a. is Rs. 331.

Interest then Principal

331 1000

49.65 ( ? )

$\therefore \frac{49.65 \times 1000}{331}$ = Rs. 150

P = Rs. 150

(6) If the compound interest on a certain sum for 2 years at 15 % per annum be Rs. 903, what would be the sum ?

Soln. Let P = Rs. 400

$\therefore C.I.=\left [P\left (1+\frac{R}{100} \right )^{N}-1 \right ]$

$=400\left [\left (\frac{115}{100} \times \frac{115}{100} \right )-1 \right ]$

=Rs. 129

C.I. then P

R.s. 129 R.s. 400

R.s. 903 (?)

$\therefore Sum=\frac{903 \times 400}{129}=R.s. 2800$

(7) A sum of money 5 times it self at C. I. in 9 yrs. When will it become 125 times ?:

Soln. 9 years $\large \Rightarrow$ 5 years.

Another 9 years $\large \Rightarrow$ 5 times of 5 times = 25 times.

& Another 9 years $\large \Rightarrow$ 5 times of 25 times = 125 times.

$\therefore$ Total time = 27 years.

(8) If Rs. 10,000, amounts to Rs. 20736 in 4 years at compound interest. What will Rs. 10,000 amount to in half that time ?

Soln. 20736 = 10000 $\left (1+\frac{R}{100} \right )^{4}$

$\therefore$ 2.0736 = $\left (1+\frac{R}{100} \right )^{4}$

$\therefore$ $\sqrt{2.0736}$ = $\left (1+\frac{R}{100} \right )^{2}$

Now, A = P $\left (1+\frac{R}{100} \right )^{2}$

= 10000 $\times$ 1.44

= Rs. 14400

The sum of money put out at R % C. I., will double in :

N = $\frac{72}{R}$