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What annual payment will discharge a debt of Rs. 6450 due in 4 years at 5% per annum?
Answer is 1500 but how is it?
A. Rs.1500
B. Rs.1400
C. Rs.1800
D. Rs.1600
Answer is 1500 but how is it?
A. Rs.1500
B. Rs.1400
C. Rs.1800
D. Rs.1600
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06 Jun 2015, 20:54
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omi0855
Point 1: It's not a GMAT like question because neither does it have 5 option choices nor does GMAT ask a question which involves a lot of calculation like it does so in case you are referring some some practice material for GMAT which includes such questions the BEWARE.
Point 2: The Annual payment can't be 1500 because 1500x4 = 6000 which is less than principle so how can it discharge a debt of 6450?
Point 3: This is an installment case in which the calculation is done on the following basis
The debt of Rs.6450 is to be paid in 4 equal instalments
Every Instalment has some Principle and some interest component which has different value for each instalment however the instalment amount remains same because if principle is more then Interest will be lesser and vise versa in order to keep the sum of both fixed which will be the total amount of each instalment
Instalment 1, I = P1+I1 [Here P1 is inciple and I1 is the interest component of first Instalment i.e.\(I = P1 (1+5/100)^1\)
Instalment 2, I = P2+I2 [Here P2 is inciple and I2 is the interest component of Second Instalment i.e. \(I = P2 (1+5/100)^2\)
Instalment 3, I = P3+I3 [Here P3 is inciple and I3 is the interest component of Third Instalment i.e. \(I = P3 (1+5/100)^3\)
Instalment 4, I = P4+I4 [Here P4 is inciple and I4 is the interest component of Forth Instalment i.e. \(I = P4 (1+5/100)^4\)
But P1 + P2 + P3 + P4 = 6450
i.e.\([I / 1.05] +[I / 1.05^2] + [I / 1.05^3] + [I / 1.05^4] = 6450\)
\(I [(1.05^3 + 1.05^2 + 1.05^1 + 1) / 1.05^4] = 6450\)
i.e. \(I = 6450 * 1.05^4 / [(1.05^3 + 1.05^2 + 1.05^1 + 1)]\)
i.e. \(I = 6450 * 1.21550625 / [1.157625 + 1.1025 + 1.05 +1]\)
i.e. I = 1819
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