Let each installment be Rs x
(x + (x * 12 * 1)/100) + (x + (x * 12 * 2)/100) + x = 1092
28x/25 + 31x/25 + x =1092
(28x +31x + 25x) = (1092 * 25)
84x = 1092 * 25
x = (1092*25)/84 = 325
Each installment = 325
Simple Interest
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newgmattest
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Interesting question Neya!
"discharge a debt" = repay full principal + all interest (and, in the real world, any associated frictional costs /fees as may apply).
We can look at this in 3 parts:
1. GMAT solution (shoot from the hip)
2. Financial modeling (a bit of it) for simple interest
3. Financial modeling (a little bit more) for compound interest - (MBA level finance courses usually cover this!)
#1: GMAT solution (shoot from the hip)
1092 + 12% (use 10% and 1100 for approximation) for 3 years
Appears to be 1100 + 330 ~ 1400
(yes, we bear in mind that equal annual payments actually lower overall interest)
1400/3 is greater than 400
so lets test highest value answer choice of 400 per year
year 1: 400 paid => Approx 130 (1092*12%) in interest and therefore 270 of principal paid
year 2: 400 paid => Approx 100 (822*12%) in interest and therefore +300 of principal paid
year 3: 400 paid ~ cannot cover 522 of remaining principal
=> 400 annual installment is lower than required
Hence: 5 None of these
==============================================
#2: Financial modeling (a bit of it) for simple interest
E (equal periodical payment)for n periods = P/[1/(1+r) + 1/(1+2r) + 1/(1+3r) ....... + 1/(1+nr)]
r= simple interest rate per period and P= principal
In this case E = 1092/(1/1.12 + 1/1.24 + 1/1.36) = 448.53
================================================
#3: Financial modeling (a little bit more) for compound interest
E (equal periodical payment)for n periods = P*r*(1+r)^n/(((1+r)^n)-1)
r= compund interest rate per period and P= principal
In this case E = 1092*0.12*(1+0.12)^3/(((1+0.12)^3) -1) = ~455
Btw, what is the source of this question?
...and hope this explanation helps
"discharge a debt" = repay full principal + all interest (and, in the real world, any associated frictional costs /fees as may apply).
We can look at this in 3 parts:
1. GMAT solution (shoot from the hip)
2. Financial modeling (a bit of it) for simple interest
3. Financial modeling (a little bit more) for compound interest - (MBA level finance courses usually cover this!)
#1: GMAT solution (shoot from the hip)
1092 + 12% (use 10% and 1100 for approximation) for 3 years
Appears to be 1100 + 330 ~ 1400
(yes, we bear in mind that equal annual payments actually lower overall interest)
1400/3 is greater than 400
so lets test highest value answer choice of 400 per year
year 1: 400 paid => Approx 130 (1092*12%) in interest and therefore 270 of principal paid
year 2: 400 paid => Approx 100 (822*12%) in interest and therefore +300 of principal paid
year 3: 400 paid ~ cannot cover 522 of remaining principal
=> 400 annual installment is lower than required
Hence: 5 None of these
==============================================
#2: Financial modeling (a bit of it) for simple interest
E (equal periodical payment)for n periods = P/[1/(1+r) + 1/(1+2r) + 1/(1+3r) ....... + 1/(1+nr)]
r= simple interest rate per period and P= principal
In this case E = 1092/(1/1.12 + 1/1.24 + 1/1.36) = 448.53
================================================
#3: Financial modeling (a little bit more) for compound interest
E (equal periodical payment)for n periods = P*r*(1+r)^n/(((1+r)^n)-1)
r= compund interest rate per period and P= principal
In this case E = 1092*0.12*(1+0.12)^3/(((1+0.12)^3) -1) = ~455
Btw, what is the source of this question?
...and hope this explanation helps
