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Mr. Paul borrows Rs. 20000 on condition to repay with C.I at 5% p.a. in annual installments of Rs. 2000 each. The number of years for the debt to be paid off is
- a)10 yrs.
- b)12 yrs.
- c)11yrs.
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Mr. Paul borrows Rs. 20000 on condition to repay with C.I at 5% p.a. i...
Present value of annuity regular
pv=A* [((1+I)^n -1)/(I*(1+I)^n]
20000=2000* [((1+0.05)^n -1)/(0.05*(1+0.05)^n]
(1.05)^n-1/(1.05)^n=10*0.05
1-1/(1.05)^n=0.5
-1/(1.05)^n= -0.5
Reciprocal
(1.05)^n=2
Taking log both sides=== n log(1.05)=log2
n=log2/log 1.05
Answer n= 14.2 years
So D is correct
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Mr. Paul borrows Rs. 20000 on condition to repay with C.I at 5% p.a. i...
Given:
Principal amount, P = Rs. 20000
Rate of interest, R = 5% p.a.
Annual installment, A = Rs. 2000
We need to find the number of years for the debt to be paid off.
Let us first calculate the amount to be paid back at the end of each year.
The amount to be paid back at the end of the first year will be the principal amount plus interest for one year, i.e.,
P + (R/100)P = 20000 + (5/100)20000 = Rs. 21000
The amount to be paid back at the end of the second year will be the amount to be paid back at the end of the first year plus interest for one year on the remaining balance, i.e.,
21000 + (R/100)(20000 - 2000) = 21000 + (5/100)18000 = Rs. 21900
Similarly, we can calculate the amount to be paid back at the end of each year as follows:
- At the end of the third year: 21900 + (R/100)(18000 - 2000) = 22785
- At the end of the fourth year: 22785 + (R/100)(16000 - 2000) = 23664.25
- At the end of the fifth year: 23664.25 + (R/100)(14000 - 2000) = 24537.46
- At the end of the sixth year: 24537.46 + (R/100)(12000 - 2000) = 25404.33
- At the end of the seventh year: 25404.33 + (R/100)(10000 - 2000) = 26264.63
- At the end of the eighth year: 26264.63 + (R/100)(8000 - 2000) = 27118.09
- At the end of the ninth year: 27118.09 + (R/100)(6000 - 2000) = 27964.45
- At the end of the tenth year: 27964.45 + (R/100)(4000 - 2000) = 28803.46
- At the end of the eleventh year: 28803.46 + (R/100)(2000 - 2000) = 29634.86
We can see that the amount to be paid back at the end of the eleventh year is greater than the installment amount of Rs. 2000. Hence, the debt cannot be paid off in 11 years.
Similarly, we can calculate the amount to be paid back at the end of each year for the twelfth year as follows:
- At the end of the twelfth year: 29634.86 + (R/100)(0 - 2000) = 29634.86 - 100 = 29534.86
We can see that the amount to be paid back at the end of the twelfth year is less than the installment amount of Rs. 2000. Hence, the debt can be paid off in 12 years.
Therefore, the correct answer is option (d) None of these.
Principal amount, P = Rs. 20000
Rate of interest, R = 5% p.a.
Annual installment, A = Rs. 2000
We need to find the number of years for the debt to be paid off.
Let us first calculate the amount to be paid back at the end of each year.
The amount to be paid back at the end of the first year will be the principal amount plus interest for one year, i.e.,
P + (R/100)P = 20000 + (5/100)20000 = Rs. 21000
The amount to be paid back at the end of the second year will be the amount to be paid back at the end of the first year plus interest for one year on the remaining balance, i.e.,
21000 + (R/100)(20000 - 2000) = 21000 + (5/100)18000 = Rs. 21900
Similarly, we can calculate the amount to be paid back at the end of each year as follows:
- At the end of the third year: 21900 + (R/100)(18000 - 2000) = 22785
- At the end of the fourth year: 22785 + (R/100)(16000 - 2000) = 23664.25
- At the end of the fifth year: 23664.25 + (R/100)(14000 - 2000) = 24537.46
- At the end of the sixth year: 24537.46 + (R/100)(12000 - 2000) = 25404.33
- At the end of the seventh year: 25404.33 + (R/100)(10000 - 2000) = 26264.63
- At the end of the eighth year: 26264.63 + (R/100)(8000 - 2000) = 27118.09
- At the end of the ninth year: 27118.09 + (R/100)(6000 - 2000) = 27964.45
- At the end of the tenth year: 27964.45 + (R/100)(4000 - 2000) = 28803.46
- At the end of the eleventh year: 28803.46 + (R/100)(2000 - 2000) = 29634.86
We can see that the amount to be paid back at the end of the eleventh year is greater than the installment amount of Rs. 2000. Hence, the debt cannot be paid off in 11 years.
Similarly, we can calculate the amount to be paid back at the end of each year for the twelfth year as follows:
- At the end of the twelfth year: 29634.86 + (R/100)(0 - 2000) = 29634.86 - 100 = 29534.86
We can see that the amount to be paid back at the end of the twelfth year is less than the installment amount of Rs. 2000. Hence, the debt can be paid off in 12 years.
Therefore, the correct answer is option (d) None of these.
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Mr. Paul borrows Rs. 20000 on condition to repay with C.I at 5% p.a. in annual installments of Rs. 2000 each. The number of years for the debt to be paid off isa)10 yrs.b)12 yrs.c)11yrs.d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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