5. Ramesh invests `12800 for three years at the rate of 10% per annum compound interest. Find :
(i) (ii) (iii)
The sum due to Ramesh at the end of the first year.
The interest he earns for the second year.
The total amount due to him at the end of the third year.
Answers
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
It is given that
Principal = ₹ 12800
Rate of interest = 10% p.a.
(i) We know that
Interest for the first year = (12800 × 10 × 1)/ 100
= ₹ 1280
So the sum due at the end of first year = 12800 + 1280
= ₹ 14080
(ii) Principal for second year = ₹ 14080
So the interest for the second year = (14080 × 10 × 1)/ 100
= ₹ 1408
(iii) We know that
Sum due at the end of second year = 14080 + 1408
= ₹ 15488
Here
Principal for third year = ₹ 15488
Interest for the third year = (15488 × 10 × 1)/ 100
= ₹ 1548.80
So the total amount due to him at the end of third year = 15488 + 1548.80
= ₹ 17036.80