A sum of $6600 was taken as loan. This is to be repaid in two annual

Question

A sum of $6600 was taken as loan. This is to be repaid in two annual installments. The rate of interest is 20%, which compounded annually. Find the value of each installment.

A. 4320
B. 4230
C. 4220
D. 4400
E. 4380

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chetan2u · Accepted Answer

You could also do it in another way.

Let x be the yearly installment.

1^{st}  Year 
Due at the end of year -  6600*1.2=7920 
 After paying x, the left amount  =  7920-x

2^{nd}  Year 
Due at the end of year -  (7920-x)*1.2 
 After paying x, the left amount  = 0, so  x=(7920-x)*1.2 
 x=(7920-x)*1.2=9504-1.2x 
 2.2x=9504......x=\frac{9504}{2.2}=4320

A

CrackverbalGMAT · Answer

When doing questions based on equal installments compounded annually, then

P = \frac{x}{(1 + \frac{r}{100})^1} + \frac{x}{(1 + \frac{r}{100})^2} + ... + \frac{x}{(1 + \frac{r}{100})^n}

Where P = Principal Amount borrowed

x = Value of each installment

n = Number of years.

In the above question, P = 6600, r = 20% and n = 2

6600 = \frac{x}{(1 + \frac{20}{100})^1} + \frac{x}{(1 + \frac{20}{100})^2}

6600 = \frac{x}{(\frac{12}{10})^1} + \frac{x}{(\frac{12}{10})^2}

6600 = \frac{10x}{12} + \frac{100x}{144}

6600 = \frac{120x + 100x}{144} = \frac{220x}{144}

x = \frac{6600 * 144}{220} = 4320

Option A

Arun Kumar

rajatchopra1994 · Answer

Explanation:
Formula: x/(1+R/100)^T

x/(1+20/100)^1 + x /(1+20/100)^2 = 6600
x/(6/5)^1 + x/(6/5)^2 = 6600
5x/6 + 25x/36 = 6600
55x/36 = 6600
x = (6600×36)/55
x = 4320

IMO-A

Numairrr · Answer

Hi could someone kindly clarify which formula we would use in this question and why?

Fdambro294 · Answer

(1st) Chart the sequence of Events

We will receive $6,600 the 1st year

throughout the year 20% Interest will accrue such that at this point, by the END of the 1st Year, we will have to pay back:

$6,600 * (1.2) = $6,600 * (6/5) -----> in Total

However, we are breaking up the Payments we pay back Each Year in 2 Equal Installments. Let the amount we pay back at the End of Year 1 = $X

Beg of Year 1: $6,600

Throughout Year 1: $6,600 * (6/5) is the amount we have to pay back so far

END of Year 1 we pay Back $X Installment so the amount Remaining:

$6,600 * (6/5) - $X

Beginning of Year 2 the Amount we still owe from the Loan is:
$6,600 * (6/5) - $X

Throughout Year 2 we will have to pay back 20% Interest on top of the Remaining Money we still owe:

* (6/5)

END of Year 2:

we want the Installment we pay back to EQUAL the Same Amount we paid back at the end of Year 1 (the Question says 2 Installments)

Therefore, the Amount we pay back at the End of Year 2 should be:

* (6/5) = $X

and now we have paid back the loan in 2 Equal Installments = $X

Q: What is the amount of the Installment? 
or
What is $X = ?

Use the Equation Set up at the End of Year 2 to Solve for $X

* (6/5) = X

----Distribute (6/5) through the Brackets-----

(6,600) * (6/5) * (6/5) - X * (6/5) = X

----Add: X * (6/5) to Each Side of the Equation----

(6,600) * (6/5) * (6/5) = (11/5) * X

----Cancel a 5 in the Denominator on Each Side of the Equation (i.e., Multiply Both Sides by *5)-----

(6,600) * (6/5) * (6) = (11) * X

---Cancel a Factor of 11 in the Numerator on Each Side of the Equation (i.e., Divide Both Sides by /11) -----

(600) * (6/5) * (6) = X

Solving For X ----->

(120) * (6) * (6) = (720) * (6) = 4,320

The Installment Payments Each Year on the Loan = $4,320

-A-

Tricky Question unless you know the Formula for Installment Payments on a Loan....

samarpan.g28 · Answer

P(1+r/100)^n=Total amount. So P = Total amount/(1+r/100)^n where P=6600. Let total amount=x.
{x/(1+20/100)}+{x/(1+20/100)^2}=6600 or, x=4320(A).

StacyArko · Answer

Hi  chetan2u , kindly assist. Why is the present value of an annuity formula not working for this question? Thank you.

sameeb · Answer

Can this question be expected in GMAT?

Krunaal · Answer

Questions on the topic of percents and interests are a part of GMAT syllabus. It is not possible to say if any particular type of question you will or will not see on the test day.

A sum of $6600 was taken as loan. This is to be repaid in two annual

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