What annual payment will discharge a debt of Rs.7620 due in 3 years at 16 2/3% per annum interest?
A. 5430
B. 4430
C. 3430
D. 2430
Solution(By Examveda Team)
Let each installment beRs.x.
[x/(1+(50/3*100))]+ [x/(1+(50/3*100))^2] + [x/(1+(50/3*100))^3] =7620 [Short - Cut]
(6x/7)+(36x/49)+(216x/343)=7620.
294x+252x+216x=7620*343.
x=(7620*343/762)=3430.
Amount of each installment=Rs.3430
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A debt of Rs. X due in 3years at y% interest rate. In agarwal this X amoumt is considered somwhere as present value and somewhere as future value. What is the correct consideration?
But here 7620 is not the present worth, it is the amount to be paid in 3 years that is future worth.
Assume we have taken a loan at period 0 and have to pay installments at the end of 1, 2, 3 periods of X each.
Now loan amount plus the interest on the total loan amount P at R% rate for 3 periods is equal to all the Installment and interests earned for the remaining period. That is the Installment.
First period earn 3 period's Interest(Say 1st year, 2nd year and 3rd year.)
Second period earn 2 period interest (2nd year and 3rd year)and so on. Thus it can be calculated as:
P*[1 +(R/100)]^4 = P*[1 +(R/100)]^2 + P*[1 +(R/100)]^1 + X.
Otherwise You can calculate through the Present Value Method Which has been used in other solution.
Rs. 3430.
Dear Teamexamveda would u pls exlain more elaborately.pls mention how installment deducted frm every year?...