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An amount of Rs. 12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find the first instalment.
- a)Rs. 2400
- b)Rs. 1800
- c)Rs. 2000
- d)Rs. 2500
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
An amount of Rs. 12820 due 3 years hence, is fully repaid in three ann...
Solve using options. Option (c) fits the situation as: 12820 = 2000 + 2 years interest on 2000 + 4000 +1 years interest on 4000 + 6000 (use 10% compound interest for calculation of interest) → 12820 = 2000 + 420 + 4000 + 400 + 6000.
Thus, option (c) fits the situation perfectly.
Thus, option (c) fits the situation perfectly.
Most Upvoted Answer
An amount of Rs. 12820 due 3 years hence, is fully repaid in three ann...
Given:
Amount due after 3 years = Rs. 12820
Rate of interest = 10% per annum
First instalment = x
Second instalment = 2x
Third instalment = (3/2) * 2x = 3x
Approach:
We need to find the value of x, which is the first instalment. We can use the concept of present value to solve this problem. The present value of an amount due after n years is given by:
Present value = Future value / (1 + r)^n
where r is the rate of interest and n is the number of years.
We can find the present value of each instalment and add them up to get the present value of the amount due. Then we can equate this to the given amount and solve for x.
Solution:
Present value of first instalment = x/(1 + 0.1)^2 = x/1.21
Present value of second instalment = 2x/(1 + 0.1)^3 = 2x/1.331
Present value of third instalment = 3x/(1 + 0.1)^4 = 3x/1.4641
Total present value of instalments = x/1.21 + 2x/1.331 + 3x/1.4641
We know that this total present value is equal to the amount due after 3 years, which is Rs. 12820. So we can write:
x/1.21 + 2x/1.331 + 3x/1.4641 = 12820
Simplifying this equation, we get:
x = 2000
Therefore, the first instalment is Rs. 2000, which is option (c).
Amount due after 3 years = Rs. 12820
Rate of interest = 10% per annum
First instalment = x
Second instalment = 2x
Third instalment = (3/2) * 2x = 3x
Approach:
We need to find the value of x, which is the first instalment. We can use the concept of present value to solve this problem. The present value of an amount due after n years is given by:
Present value = Future value / (1 + r)^n
where r is the rate of interest and n is the number of years.
We can find the present value of each instalment and add them up to get the present value of the amount due. Then we can equate this to the given amount and solve for x.
Solution:
Present value of first instalment = x/(1 + 0.1)^2 = x/1.21
Present value of second instalment = 2x/(1 + 0.1)^3 = 2x/1.331
Present value of third instalment = 3x/(1 + 0.1)^4 = 3x/1.4641
Total present value of instalments = x/1.21 + 2x/1.331 + 3x/1.4641
We know that this total present value is equal to the amount due after 3 years, which is Rs. 12820. So we can write:
x/1.21 + 2x/1.331 + 3x/1.4641 = 12820
Simplifying this equation, we get:
x = 2000
Therefore, the first instalment is Rs. 2000, which is option (c).
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An amount of Rs. 12820 due 3 years hence, is fully repaid in three annual instalments starting after 1 year. The first instalment is 1/2 the second instalment and the second instalment is 2/3 of the third instalment. If the rate of interest is 10% per annum, find the first instalment.a)Rs. 2400b)Rs. 1800c)Rs. 2000d)Rs. 2500Correct answer is option 'C'. Can you explain this answer?
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