DS Question 1 - Mar 21 A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the account was opened. Once the balance reached $1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate? (1) The account earned exactly $25 in interest at the 2.5% rate. (2) The account was open for exactly three years. Source: Official Guide | Difficulty: Medium
stem: Is, interest @2% p.a. > interest @2.5% p.a. ?
or I1 > I2 ?
if "m" is the principal amount to start with and for "n" days the account operated
$1000 will be the new amount at the end of 2% interest scenario.
1000 = m(1+2/(100*365))^t , assuming this goes on for "t" days
we get value of "m" if we have "t"
then interest, I1 = m(1+2/(100*365))^t - m
another case where 2.5% is interest rate., 1000 is the principal to start with
then, total interest earned, I2= 1000(1+2.5/(100*365))^n-t - 1000
WE need value of t,n to make a comparison;
both statements individually are not sufficient;
statement1: we get to know I2 = 25, so, "n-t" can be known
statement2: we get time of 3 years, that is we can say "n" is given in years. so we can get "t"
combine both, we have all the info we need, so option C