Harikrushna Kotadiya wrote:

Elliot and Faye invest $5000 each in different banks. Elliot earns annual rate of interest 12% compounded monthly and Faye earns annual rate of interest 12% compounded quarterly. If after 6 months Elliot earns a total interest of E, and Faye earns a total interest of F, which of the following must be true?

A. E=F

B. E>F

C. E<F

D. E=$300

E. F=$300

No need to calculate, if compound interest is familiar. (If not, see the rule below.

) Principal amounts, interest rates, and time are identical. E gets paid more times than F. E will be greater than F.

The rule is: All else being equal (principal, interest rate, and time period), whoever gets paid "interest on interest" more frequently has the highest rate of return and highest future value over time.

If more frequent installments = greater future value, then Elliott wins. Elliott gets paid compounding interest 12 times a year, or 6 times in 6 months. Faye gets paid compounding interest 4 times a year, or 2 times in six months.

No matter what, over time, Elliott earns more "interest on interest."

But if you sense that the difference is not huge (and it is not here - six months is too short a time), and you want to be sure . . . you can choose an easier principal amount and round a little.

$10,000 at 12%? Choose a big principal. For rate, stay with 12 percent for ease of division.

E gets .12/12 = .01 every month

F gets .12/4 = .03 every 3 months

Amount with interest added in, for months 1-6:

E: 10100, 10201, 10303, 10406, 10510,

10615F: 10000, 10000, 10300, 10300, 10300,

10,609E > F

ANSWER B

Actual difference here is not huge. After six months:

Elliott has $5,307.60

And Faye has $5,304.50

Still, E has about $3.00 more. That is all that matters. Over time, E will be greater than F by quite a bit.

_________________

At the still point, there the dance is. -- T.S. Eliot

Formerly genxer123