Question Bank - Quant (Fractions Ratios) "Donald Invests..."

[akhila.iruku]

Hi there!

My question is from the question bank which seems straightforward:

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?


$1500
$1750
$2000
$2500
$3000

I picked $3000 because $2500 would give a return of exactly $100 whereas the question asks "to earn over $100 in interest...". Am I reading too much into it or is this an error in the question bank? Thanks!

[RonPurewal]

Hi there!

My question is from the question bank which seems straightforward:

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly.

^^ This means that you have to do the interest calculations every 1/4 year. Since the annual percentage is given as 8%, that means you're actually adding 2% per quarter.

Half a year is two quarters.

If you invest $2500 initially, then, after one quarter, you gain 2% of $2500 = $50 in interest.
Now there's $2550 in the bank.
After the second quarter, you gain 2% of $2550, which is ... a little more than $50. (We don't care about the exact amount, because all we need to know is that it's more than $50. Which it definitely is, because $50 was 2% of a smaller amount.)