Question

A sum of money invested at compound interest amounts to Rs 10000 in 4 years and to Rs 12000in 5 years. Find the amount that the sum will yield After 6 years

Answer 1

||✪✪ QUESTION ✪✪||

A sum of money invested at compound interest amounts to Rs 10000 in 4 years and to Rs 12000in 5 years. Find the amount that the sum will yield After 6 years ?

|| ✰✰ ANSWER ✰✰ ||

Lets Try to Solve with Basic Method First :-

Given That, A sum of money invested at compound interest amounts to Rs 10000 in 4 years and to Rs 12000 in 5 years.

So, we can say That, in 1 year From 4Th year to 5th year we get an compound interest of Rs.2000 on Rs.10000 . ( As we know That, In CI we get interest on Interest ).

So, we can say That :-

→ Rate % = (2000*100)/(10000) = 20% .

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Now , we Have ,

→ Rate = 20%

→ Time = 4 years .

→ Amount = Rs.10000

→ Principal = Let P .

we know The formula for Compound interest :-

→ Amount = Principal * [ 1 + (R/100)]^T

Putting all values now , we get :-

→ 10000 = P [ 1 + (20/100)]⁴

→ 10000 = P( 1 + 1/5)⁴

→ 10000 = P(6/5)⁴

→ P = (10000*5*5*5*5)/(6*6*6*6)

→ P = Rs.4822.53.

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Now, we Have To Find amount that the sum will yield After 6 years .

So, Again using same formula now, with Time as 6 years we get,

→ Amount = 4822.53 [ 1 + (20/100)]^6

→ amount = 4822.53(6/5)^6

→ Amount = Rs.14400 .(Ans).

Hence, the amount that the sum will yield After 6 years is Rs.14400.

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❁❁ Shortcut Trick.. ❁❁

Now, After Find Rate of Interest we can say that, since compound interest is basically interest on interest.

And, we also have Same Principal now, we just have to Find how much The amount will be after 6 years.

we have now :-

→ Amount after 5 years = Rs.12000

→ Rate = 20% .

So,

→ Amount after 6 years = 12000 + interest on 12000 at 20%

So,

→ Amount after 6 years = 12000 + (12000*20/100) = 12000 + 2400 = Rs.14400.

Hence, the amount that the sum will yield After 6 years is Rs.14400.

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Answer 2

Answer:

The amount that the sum will yield after 6 years is Rs 14,400

Step-by-step explanation:

As per the data given in the question,

We have,

Amount increases by 2000 from 4th year to 5th year where 10000 will act as principle.

So, rate of interest will be:

$\frac{2000}{10000} \times 100 = 20\%$

Now, we know,

Amount = 10000

Rate = 20%

Principle = ?

Time = 4 years

So, by applying formula we will get Principle:

$A= P[1+(R/100)]^{4} \\10000=P[1+(20/100)]^{4} \\10000=P(1.2)^{4}\\ P=\frac{1000}{(1.2)^{4}} \\P=\frac{1000}{2.0736}\\P=4822.53$

So, the principle is Rs 4822.53

Now, Amount in 6 years will be:

$A=P[1+(R/100)]^{6}\\ =4822.53[1.2]^{6}\\=14400$

Therefore,

The amount that the sum will yield after 6 years is Rs 14,400

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