Ricardo deposits $1,000 in a bank account that pays 10%

Question

Ricardo deposits $1,000 in a bank account that pays 10%
interest, compounded semiannually. Poonam deposits $1,000 in
a bank account that pays 10% interest, compounded annually.
If no more deposits are made, what is the difference between
the two account balances after 1 year?

A. $2.50
B. $10
C. $5
D. $15
E. $100

PS: This is todays' Deltacourse question. I am posting it here, so that non-subscribers of Deltacource can also benefit.

GMATT73 · Answer

I get $110, which is not an answer choice. E would have to be a rounded off guess.

Then again, it is past midnight after 12 hours of work and I am clearly math incompetent...

laxieqv · Answer

R deposits 1,000 so for the first semiannual period his deposit is 1,000+1,000*10%= 1,100. For the second semi-year, his deposit is : 1,100+1,100*10%= 1210. 
P deposits 1,000 with annual interest of 10%----> after one year, his deposit is 1,100 
The difference is 110. I agree with GMATT73!

desiguy · Answer

Another one for $110. Is this an estimation question or something? Maybe the last choice is supposed to be 110 instead of 100....?

sudhagar · Answer

Let me give the formula for compound interest:

The formula for compound interest is
(final balance) = principal * (1 + (interest rate) / N)(time * N)

Where N is the number of times the interest is compounded annually

I hope guys can crack it now.

PS: I am following a phased approach to kindle the thought process

MsStephanie · Answer

I did this another way

 

For the bank account compounded semiannually, the interest is 5% for each time period.

for the first 6 months, R earns  1,000(1.05) = 1,050 
for the second 6 months, he earns another 5%  1,050(1.05) = 1,102.50 
his grand total is now $1,102.50

For the bank account compounded annually, the interest is a straight 10%
 1,000(1.10) = $1,100 

You are asked for the difference between the two account balances after one year..

$1,100 - 1,102.50 = $2.50

A is the answer?

pavrnd · Answer

A) 2.50

Account1: Interset for first 6 months = 1000*5/100 = 50
Interst for next 6 months = 1050*5/100 = 52.50

Account2: Interest = 100

Diff = 2.50

sudhagar · Answer

OA is A.

MsStephanie & pavrnd's method can also be employed. But here is how you would the compound interest formula:

After one year, Ricardo's balance is

final balance = $1,000 * (1 + (.10 / 2)(1 * 2)
final balance = $1,000 * 1.052
final balance = $1,000 * 1.1025
final balance = $1,102.50

After one year, Poonam's balance is

final balance = $1,000 * (1 + (.10 / 1))(1 * 1)
final balance = $1,000 * (1.10)1
final balance = $1,000 * 1.10
final balance = $1,100

The difference between the accounts

difference = $1,102.50 - $1,100
difference = $2.50

Ricardo deposits $1,000 in a bank account that pays 10%

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