Question

Ramesh invests rupees 12800 for 3 years at the rate of 10% per annum compound interest. Find i) the sum due to ramesh at the end of first year. ii) the interest he earns for second year. iii) the total amount due to him at the end of three years ​

Answer 1

Answer:

1.14080

2.1408

3.17036.8

Step-by-step explanation:

The amount he invested=12800

Number of years=3

Rate of interest per annum=10%

Interest generated for first year

12800*10/100=1280

Since it is compound interest the sum he gets at the end of first year is 12800+1280=14080

Interest generated for second year

14080*10/100=1408

So 1408 is the interest generated for second year and the total becomes 15488

Interest generated for third year

15488*10/100=1548.8

So the total earnings by the end of three years are

15488+1548.8=17036.8

Answer 2

Answer:

₹14080

₹1408

₹17036.8

Step-by-step explanation:

Given data:

Principal amount (P) = ₹ 12800

Rate of interest (r) = 10% per annum

Time period (t) = 3 years

For the first year, the amount of interest would be 10% of principal amount

Interest at end of first year = 10% of 12800

                                               = 10/100 x 12800

                                               = ₹ 1280

Hence, total amount gained = Principal + Interest

                                                          = ₹ 12800 + ₹ 1280

                                                          = ₹ 14080

Or

Using mathematical formula for calculating amount due to compound interest

S = P[1 + r/100]ⁿ

where,

S = Amount

P = Principal

r = rate of interest

n = time period

Substituting all values

S = 12800 [1 + 10/100]1

  = 12800 x 1.1

  =₹ 14080

When the principal is compounded, the interest for consecutive year is calculated on the basis of total amount accumulated in previous year.

Thus, for 2nd year, the interest would be added on the total amount accumulated during first year

Interest earned during 2nd year = 10% of 14080

                                                      = ₹ 1408

Amount at the end of 2nd year = ₹ 14080 + ₹1408

                                                    = ₹ 15488

Similarly, interest for the 3rd year = 10% of 15488

                                                       = ₹ 1548.8

Thus, Total amount at the end of 3rd year = ₹15488 + ₹1548.8

                                                                      = 17036.8

OR

Using mathematical formula for calculating amount due to compound interest

S = P[1 + r/100]ⁿ

Substituting all values

S = 12800 [1 + 10/100]³

  = 12800 x 1.331

  =₹ 17036.8