At what rate of interest will a sum of money amount to 7/4 of itself in 8 years and 4 months

Question 5 Simple and Compound Interest Exercise 8.1

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Answer:

(i) Here,

I = Rs 2356.25

R =7 \frac{1}{4} \% \text { p.a }

= 29 / 4 % p.a.

T = 2 \frac{1}{2} \text { years }

= 5 / 2 years

Hence,

P = (I × 100) / (R × T)

= Rs (2356.25 × 100) / (29 / 4) × (5 / 2)

On further calculation, we get,

= Rs (2356.25 × 100 × 4 × 2) / (29 × 5)

= Rs (235625 × 8) / (29 × 5)

We get,

= Rs (47125 × 8) / 29

= Rs 1625 × 8

= Rs 13000

(ii) Amount (A) = Rs 11300

Rate (R) = 4% p.a.

Time (T) = 3 years 3 months

=3 \frac{3}{12} \text { years }

=\frac{3}{4} \text { years }

= 13 / 4 years

Let the principal be Rs x

Hence,

S.I. = (P × R × T) / 100

= Rs (x × 4 × 13) / (100 × 4)

We get,

= Rs 13x / 100

Then,

Amount = Principal + Simple Interest

= Rs x + Rs 13x / 100

= Rs (x + 13x) / 100

We get,

= Rs (100x + 13x) / 100

= Rs (113x / 100)

But, the amount given is Rs 11300

Hence,

113x / 100 = 11300

x = 11300 × 100 / 113

x = 100 × 100

We get,

x = 10000

Therefore, principal (P) = Rs 10000

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