3. A certain sum amounts to 5,292 in two
years and 5,556,60 in three years, interest
being compounded annually. Find:
(i) the rate of interest
(ii) the original sum.
without using formula
Answers
Answer:
answer is in attachment
Correct question!
A certain sum amounts to 5,292 in two
years and 5,556.60 in three years, interest
being compounded annually. Find:
(i) the rate of interest
(ii) the original sum.
without using formula
Solution!!
The amount after two years and the amount after three years is given to us in the question. The amount after the second year becomes the principal in the third year. So, let's take the time period from second year to third year.
Principal (P) = Rs 5292
Time (T) = 1 year
Amount after third year = Rs 5556.60
Let's find out the compound interest.
Compound Interest (CI) = Amount - Principal
CI = Rs 5556.60 - Rs 5292
CI = Rs 264.60
We know that compound interest for one year equals simple interest for one year. So,
SI = Rs 264.60
Let's use the simple interest formula and find the rate of interest.
SI = (P × R × T)/100
Here,
P → Principal
R → Rate of interest
T → Time
SI → Simple interest
264.60 = (5292 × R × 1)/100
264.60 × 100 = 5292 × R × 1
26460 = 5292 × R
R = 26460 ÷ 5292
R = 5
Hence,
Rate of interest (R) = 5%
Now, we have to find the sum which was invested in the first year. We know the amount after the second year.
First year:-
Principal (P) = x
Rate of interest (R) = 5%
Time (T) = 1 year
Interest = (P × R × T)/100
Interest = (x × 5 × 1)/100
Interest = x/20
Amount = Principal + Interest
Amount = x + x/20
Amount = (20x + x)/20
Amount = 21x/20 = 1.05x
Second year:-
The amount in the first year becomes the principal in the second year.
Principal (P) = 1.05x
Time (T) = 1 year
Rate of interest (R) = 5%
Interest = (P × R × T)/100
Interest = (1.05x × 5 × 1)/100
Interest = 1.05x/20
Interest = 0.0525x
We know the amount after the second year.
Amount = Principal + Interest
5292 = 1.05x + 0.0525x
5292 = 1.1025x
x = 5292 ÷ 1.1025
x = 4800
Hence, the original sum which was invested in the first year was Rs 4800.
Orginal sum = Rs 4800