Question

Mahesh invests Rs.3000 for 3 years at rate of 10th p. a. Compound interest.Find the amount and the compound interest that Makesh will get after 3 years.​

Answer 1

Given :

• Principal = Rs.3000
• Rate = 10%
• Time = 3 years

To find :

• the compound interest and amount

Solution :

➝ Let's find the compound interest.

$\tt\implies \boxed{ \sf Amount = \tt P \left[ 1 + \dfrac{ R }{100} \right]^{n } }$

Here,

• P = 3000
• R = 10
• N = 3

$\tt\implies { \sf Amount = \tt 3000 \left[ 1 + \dfrac{ 10 }{100} \right]^{3 } }$

$\tt\implies { \sf Amount = \tt 3000 \left[ \dfrac{100 + 10 }{100} \right]^{3 } }$

$\tt\implies { \sf Amount = \tt 3000 \left[ \dfrac{110}{100} \right]^{3 } }$

$\tt\implies { \sf Amount = \tt 3000 \left[ \dfrac{11}{10} \right]^{3 } }$

$\tt\implies { \sf Amount = \tt 3000 \left[ \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} \right] }$

$\tt\implies { \sf Amount = \tt 3000 \left[ \dfrac{11 \times 11 \times 11}{10 \times 10 \times 10} \right]}$

$\tt\implies { \sf Amount = \tt 3 \cancel0 \cancel0 \cancel0 \left[ \dfrac{11 \times 11 \times 11}{1 \cancel0 \times 1 \cancel0 \times 1 \cancel0} \right]}$

$\tt\implies { \sf Amount = \tt 3 \left[ \dfrac{11 \times 11 \times 11}{1 \times 1 \times 1 } \right]}$

$\tt\implies { \sf Amount = \tt 3 \left[ \dfrac{1331}{1 } \right]}$

$\tt\implies { \sf Amount = \tt 3 \left[ 1331\right]}$

$\implies \tt Amount = 3 \times 1331$

$\implies \tt Amount = 3993$

• Therefore, the Amount is Rs. 3993.

Compound Interest = Amount - Principal

= 3993 - 3000

= 993

• Therefore, the Compound Interest is Rs. 993.

Answer 2

Given

• Principal = ₹3000.
• Time = 3years.
• Rate = 10% p.a.

To Find

• Amount.
• Compound Interest.

Solution

This problem is solved using simple interest method. In this method we will take out the simple interest and amount for the three years. Amount for third year will be final amount. After that we will find out the compound interest from final amount and original principal.

For the First year

Principal = ₹3000.

Rate = 10% p.a.

Time = 1year.

I = P × R × T/100

=> I = 3000 × 10 × 1/100

=> I = ₹300.

Amount = P + I = 3000 + 300 = ₹3300.

Note:-

Amount for first year = Principal for second year.

For the second year

Principal = ₹3300.

Rate = 10% p.a.

Time = 1year.

I = P × R × T/100

=> I = 3300 × 10 × 1/100

=> I = ₹330.

Amount = P + I = 3300 + 330 = ₹3630.

Note:-

Amount for second year = Principal for third year.

For the third year

Principal = ₹3630.

Rate = 10% p.a.

Time = 1year.

I = P × R × T/100

=> I = 3630 × 10 × 1/100

=> I = ₹363.

Final Amount = P + I = 3630 + 363 = ₹3993.

C.I. = Final Amount - Original Principal

=> C.I. = 3993 - 3000

=> C.I. = ₹993.

Note:-

Here compound interest is equal to the sum of interest of 3years i.e. 300 + 330 + 363 = 993.

Final Answer

• Amount that Mahesh will get = ₹3993.
• Compound Interest that Mahesh will get = ₹993.

Used Abbreviations

• P = Principal.
• R = Rate.
• T = Time.
• I = Simple Interest.
• C.I. = Compound Interest.

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