At what rate compound interest per annum will rupees 576 amount to 625 in 2 years?

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Sum

In what time will Rs 15625 amount to Rs 17576 at 4% p.a. compound interest?

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Solution

Here P = Rs.15625, A = 17576, r = 4%

Now, `"P"(1 + "r"/100)^"t"` = A

⇒ `15625(1 + 4/100)^"t"`

= 17576

⇒ `(26/25)^"t"`

= `(17576)/(15625)`

= `(26/25)^3`
By comparing powers, t = 3
Hence time is 3 years.

Concept: Concept of Compound Interest - When the Time is Not an Exact Number of Years and the Interest is Compounded Yearly

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Chapter 3: Compound Interest - Exercise 3.2

Q 8Q 7Q 9

APPEARS IN

Frank Class 9 Maths ICSE

Chapter 3 Compound Interest
Exercise 3.2 | Q 8

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It is given that

Amount = ₹ 2500

Principal = ₹ 2304

Period (n) = 2 years

Consider r% p.a. as the rate of interest

We know that

\begin{aligned} &\mathrm{A}=\mathrm{P}(1+\mathrm{r} / 100)^{\mathrm{n}}\\ &\text { It can be written as }\\ &(1+\mathrm{r} / 100)^{\mathrm{n}}=\mathrm{A} / \mathrm{P} \end{aligned}

Substituting the values

\begin{aligned} &(1+\mathrm{r} / 100)^{2}=2500 / 2304\\ &\text { By further calculation }\\ &(1+\mathrm{r} / 100)^{2}=625 / 576=(25 / 24)^{2} \end{aligned}

So we get

1 + r/100 = 25/24

r/100 = 25/24 – 1

Taking LCM

r = 100/24 = 25/6 = 4 1/6

Hence, the rate of interest is 4 1/6% p.a.

If a sum is compounded annually and becomes 676/625 times itself in 2 years, then find the rate of interest.

1. 8%
2. 10%
3. 5%
4. 4%

Answer (Detailed Solution Below)

Option 4 : 4%

Free

20 Questions 20 Marks 15 Mins

Given:

Time = 2 years

The sum becomes 676/625 itself.

Formula used:

A = P(1 + r/100)n

Where, A = Amount, P = Principal, r = Rate of interest, n = Time in years

Calculation:

Let the principal be P.

Amount will become 676P/625 in 2 years

676P/625 = P(1 + r/100)2

⇒ 676/625 = (1 + r/100)2

⇒ (26/25)2 = (1 + r/100)2

⇒ 26/25 = 1 + r/100

⇒ r/100 = 26/25 - 1

⇒ r/100 = 1/25

⇒ r = 4%

∴ The rate of interest is 4%.

Ratio of amount and principal for 2 years if the sum is compounded annually = √A ∶ √P

⇒ √676 ∶ √625

⇒ 26 ∶ 25

Rate of interest = [(26 - 25)/25] × 100

⇒ Rate of interest = (1/25) × 100

⇒ Rate of interest = 4%

∴ Rate of the interest is 4%.

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