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Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is?
Most Upvoted Answer
Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a...
Calculation of Interest and Installments
Final Answer
- The annual interest rate is 5%, which means the monthly interest rate is 5/12 = 0.4167%.
- The total interest payable on the loan is calculated using the formula: A = P(1 + r/n)^(n*t) - P, where A is the total amount payable, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
- Plugging in the values, we get A = 20000(1 + 0.05/1)^(1*t) - 20000 = 2000t.
- Therefore, the total interest payable is 2000t.
- As the loan is to be repaid in annual installments of Rs. 2000 each, the number of years it will take to pay off the loan is equal to the total interest payable divided by the annual installment amount.
- So, t = 2000t/2000 = t years.
Final Answer
- Therefore, it will take t years to pay off the loan.
- The exact value of t can be calculated by using the formula: A = P(1 + r/n)^(n*t) - P.
Community Answer
Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a...
Given that,
Periodic payment = 2000
Amount of loan = 20000
Periodic interest rate= 5% =0.05
We need to calculate the number of periods
Using formula of periodic payment
A=P\dfrac{r(1+r)^n}{(1+r)^n-1}A=P
(1+r)
n
−1
r(1+r)
n
Where, A = Periodic payment
P = Amount of loan
r = Periodic interest rate
Put the value into the formula
2000=20000\times\dfrac{0.05(1+0.05)^n}{(1+0.05)^n-1}2000=20000×
(1+0.05)
n
−1
0.05(1+0.05)
n
2000=1000\times\dfrac{(1.05)^n}{(1.05)^n-1}2000=1000×
(1.05)
n
−1
(1.05)
n
2(1.05)^n-2=(1.05)^n2(1.05)
n
−2=(1.05)
n
(1.05)^n=2(1.05)
n
=2
Taking log
ln(1.05)^n=ln(2)ln(1.05)
n
=ln(2)
n\ ln(1.05)=ln(2)n ln(1.05)=ln(2)
n=\dfrac{ln(2)}{ln(1.05)}n=
ln(1.05)
ln(2)
n=14.2\ yearsn=14.2 years
It will take 15 years to repay the loan.
Periodic payment = 2000
Amount of loan = 20000
Periodic interest rate= 5% =0.05
We need to calculate the number of periods
Using formula of periodic payment
A=P\dfrac{r(1+r)^n}{(1+r)^n-1}A=P
(1+r)
n
−1
r(1+r)
n
Where, A = Periodic payment
P = Amount of loan
r = Periodic interest rate
Put the value into the formula
2000=20000\times\dfrac{0.05(1+0.05)^n}{(1+0.05)^n-1}2000=20000×
(1+0.05)
n
−1
0.05(1+0.05)
n
2000=1000\times\dfrac{(1.05)^n}{(1.05)^n-1}2000=1000×
(1.05)
n
−1
(1.05)
n
2(1.05)^n-2=(1.05)^n2(1.05)
n
−2=(1.05)
n
(1.05)^n=2(1.05)
n
=2
Taking log
ln(1.05)^n=ln(2)ln(1.05)
n
=ln(2)
n\ ln(1.05)=ln(2)n ln(1.05)=ln(2)
n=\dfrac{ln(2)}{ln(1.05)}n=
ln(1.05)
ln(2)
n=14.2\ yearsn=14.2 years
It will take 15 years to repay the loan.
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Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is?
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Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is?.
Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. Paul borrows rs. 20000 on condition to repay it withC.I. at 5% p.a.in annual Installments of rs. 2000 each. The number of years for the debt to be paid off is?.
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