A sum of $3310 is to be paid back in 3 equal installments.

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A sum of $3310 is to be paid back in 3 equal installments. How much is each installment if the interest is compounded annually at 10% per annum.

A. 1311
B. 1331
C. 1103
D. 2331
E. 2311

OA B

[Anju@Gurome]

A sum of $3310 is to be paid back in 3 equal installments. How much is each installment if the interest is compounded annually at 10% per annum.

It is not mentioned whether the installments are monthly or annual. But looking at the options, I think it should be yearly. Now, let us assume each installment will be I.

After 1st year, amount to be paid back = 3310*(1 + 10/100) - P = 3310*(1.1) - P = 3641 - P

After 2nd year, amount to be paid back = (3641 - P)*(1 + 10/100) - P = (3641 - P)*(1.1) - P ≈ 4000 - 2.1P

After 3rd year, amount to be paid back = (4000 - 2.1P)*(1 + 10/100) - P = (4000 - 2.1P)*(1.1) - P = 4400 - 3.31P

Now, after the 3rd year, there shouldn't be any amount left to be paid back.
So, 4400 - 3.31P = 0
--> P = 4400/3.31 ≈ 4400/3.3 = 44000/33 = 4000/3 ≈ 1333 ≈ 1331

The correct answer is B.

[CSASHISHPANDAY]

the easiest method I got in my finance book
which says that
If the installment value is x after 1 year, then it equals to x/1.1 to the current value
Similarly, installment value is x after 2 year, then it equals to x/(1.1)^2 to the current value
Similarly, installment value is x after 3 year, then it contributes to x/(1.1)^3 to the current value
So, total current value =

x/1.1 + x/(1.1)^2 + x/(1.1)^3 =3310
or 3310X/1331=3310
or [spoiler]x=1331[/spoiler]
Ans 1331