Direct Problems
1. Ramesh invests 12,800 for three years at the rate of 10% per annum compound interest. Find:
(i) The sum due to Ramesh at the end of the first year.
(ii) The interest he earns for the second year.
(iii) 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
Answer:
P =Rs.12800
Rate of interest =10 %
Interest for the first year =
100
PRT
⇒
100
12800×10×1
=Rs.1280
Amount after first year=12800+1280=Rs.14080
For Second year
Principal =Rs.14080
R =10%
T =1 year
then Interest for second year=
100
PRT
⇒
100
14080×10×1
=Rs.1408