Interest

[govind_raj_76]

Trevor began his job as a bank clerk with a monthly salary of 1800 $. Out of the salary, Trevor started depositing 1300 $ in his savings account that paid interest at an annual rate of 12 % compounded monthly. What is the interest earned by Trevor at the end of 4 months ?

a) 52.53 $

b) 70.5 $

c) 112 $

d) 131 $

e) 143 $

Please help. The answer is D. I am not sure how it is D. Please advise.

[4GMAT_Mumbai]

Hi,

The thing to figure out here is: 'This is a recurring deposit. This is not a fixed deposit'.

The money deposited at the beginning of month 1 earns a monthly interest of 1% (12% / 12) on a compounded basis for 4 months.

At the end of 4 months, this accrues to = 1300 * (1 + 0.1) ^ 4

The money deposited at the beginning of month 2 earns a monthly interest of 1% (12% / 12) on a compounded basis for 3 months.

At the end of 4 months, this accrues to = 1300 * (1 + 0.1) ^ 3

The money deposited at the beginning of month 3 earns a monthly interest of 1% (12% / 12) on a compounded basis for 2 months.

At the end of 4 months, this accrues to = 1300 * (1 + 0.1) ^ 2

The money deposited at the beginning of month 4 earns a monthly interest of 1% (12% / 12) on a compounded basis for 1 month.

At the end of 4 months, this accrues to = 1300 * (1 + 0.1) ^ 1

Overall total A is Rs 5,331.30. Total P is Rs 5,200.00

Interest is Rs 131.0

[krazy800]

Trevor began his job as a bank clerk with a monthly salary of 1800 $. Out of the salary, Trevor started depositing 1300 $ in his savings account that paid interest at an annual rate of 12 % compounded monthly. What is the interest earned by Trevor at the end of 4 months ?

a) 52.53 $

b) 70.5 $

c) 112 $

d) 131 $

e) 143 $

Please help. The answer is D. I am not sure how it is D. Please advise.

Monthly Interest Rate = 1% and he makes 1300$ deposit every month!

for his 1st month deposit, interest amount = (1300*(1.01^4)) -1300 = 52.78
similarly for his second month deposit, interest amount =(1300*(1.01^3)) -1300 = 39.39
for his third month deposit, interest amount =(1300*(1.01^2)) -1300 = 26.13
for his fourth month deposit, interest amount =(1300*(1.01^1)) -1300 = 13

If u total all the above u will get 131$

HTH!

I am very much eager to see a shortcut approach to this problem

[mj78ind]

@krazy800

writing your equation another way -

I = 1300(1.01)^4 + 1300(1.01)^3 + 1300(1.01)^2 + 1300(1.01)^1 - 1300*4

We know in binomial theorem (1+x)^n = 1 + xn for very small 'x'

Thus, I = 1300(1.04+1.03+1.02+1.01) -1300 = 1300*0.1 = $130 which is pretty close

Two things this looks like a super tough one for the GMAT, however this approximate approach can help solve the problem in <2 mins