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A company borrows Rs. 10000 on condition to repay it with compound interest at 5% p.a by annual installments of Rs. 1000 each. The number of years by which the debt will be clear is
- a)14.2 yrs.
- b)10 yrs.
- c)12 yrs.
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A company borrows Rs. 10000 on condition to repay it with compound int...
solutions
Present value of annuity regular
pv=A* [((1+I)^n -1)/(I*(1+I)^n]
10000=1000* [((1+0.05)^n -1)/(0.05*(1+0.05)^n]
(1.05)^n-0.5*(1.05)^n=1
(1.05)^n=2
Taking log both sides
n=log2/log 1.05r
Answer n= 14.2 years
Most Upvoted Answer
A company borrows Rs. 10000 on condition to repay it with compound int...
Given:
Principal (P) = Rs. 10000
Rate of interest (R) = 5% p.a
Annual installment (A) = Rs. 1000
To find: Number of years it will take to clear the debt
Formula used:
Compound Interest formula:
A = P (1 + R/100)ⁿ
where,
A = Final amount
P = Principal
R = Rate of interest
n = Number of years
Calculations:
Let the number of years be 'n'
After 1st year:
Amount = Principal + Interest - Installment
= 10000 + (5/100)*10000 - 1000
= 4600
After 2nd year:
Amount = Previous amount + Interest - Installment
= 4600 + (5/100)*4600 - 1000
= 4260
Similarly, we can calculate the amount for the 3rd year, 4th year, and so on.
We need to find the value of 'n' such that the amount becomes zero.
After n years:
Amount = 0
P (1 + R/100)ⁿ = A * ((1 + R/100)ⁿ - 1) * (100/R)
10000 * (1 + 5/100)ⁿ = 1000 * ((1 + 5/100)ⁿ - 1) * (100/5)
20 (1.05)ⁿ = (1.05ⁿ - 1)
Dividing both sides by 20, we get:
(1.05)ⁿ/20 = (1.05ⁿ - 1)/20
Using trial and error method, we can find that n = 14.2 years approximately.
Therefore, the number of years it will take to clear the debt is approximately 14.2 years.
Hence, the correct option is (a) 14.2 years.
Principal (P) = Rs. 10000
Rate of interest (R) = 5% p.a
Annual installment (A) = Rs. 1000
To find: Number of years it will take to clear the debt
Formula used:
Compound Interest formula:
A = P (1 + R/100)ⁿ
where,
A = Final amount
P = Principal
R = Rate of interest
n = Number of years
Calculations:
Let the number of years be 'n'
After 1st year:
Amount = Principal + Interest - Installment
= 10000 + (5/100)*10000 - 1000
= 4600
After 2nd year:
Amount = Previous amount + Interest - Installment
= 4600 + (5/100)*4600 - 1000
= 4260
Similarly, we can calculate the amount for the 3rd year, 4th year, and so on.
We need to find the value of 'n' such that the amount becomes zero.
After n years:
Amount = 0
P (1 + R/100)ⁿ = A * ((1 + R/100)ⁿ - 1) * (100/R)
10000 * (1 + 5/100)ⁿ = 1000 * ((1 + 5/100)ⁿ - 1) * (100/5)
20 (1.05)ⁿ = (1.05ⁿ - 1)
Dividing both sides by 20, we get:
(1.05)ⁿ/20 = (1.05ⁿ - 1)/20
Using trial and error method, we can find that n = 14.2 years approximately.
Therefore, the number of years it will take to clear the debt is approximately 14.2 years.
Hence, the correct option is (a) 14.2 years.
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Community Answer
A company borrows Rs. 10000 on condition to repay it with compound int...
Try though options,
a) 14.2
b) 10
c) 12
d) none
formula, 1÷(1+I)^n.
on calculator,
1÷(1+0.05) ^ let op a) 14 as n,
press = 14 times from one,
press Grand total(G.T)
press M+,
put p.v (10000)
÷ MRC= 1010.200 which is equal to 14.2 years.
a) 14.2
b) 10
c) 12
d) none
formula, 1÷(1+I)^n.
on calculator,
1÷(1+0.05) ^ let op a) 14 as n,
press = 14 times from one,
press Grand total(G.T)
press M+,
put p.v (10000)
÷ MRC= 1010.200 which is equal to 14.2 years.
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A company borrows Rs. 10000 on condition to repay it with compound interest at 5% p.a by annual installments of Rs. 1000 each. The number of years by which the debt will be clear isa)14.2 yrs.b)10 yrs.c)12 yrs.d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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