Someone plans to invest $10,000 in an account paying 3% annual interest and compounded semi-annually. How much must he invest in another account paying 5% annual interests and compounded quarterly so that his annual income from the 2 accounts in the first year are the same?
Anyone know a shorter way to solve this problem
I tried solving it wasted too much time
There is a shorter way:
(x+y)^4 = x^4 + 4x^3 y+ 4xy^3+6x^2 y^2 + y^4
(x+y)^2 = x^2+2xy+y^2
when y is too small as compared to x then these can be reduced to
(x+y)^4 = x^4 + 4x^3 y
(x+y)^2 = x^2+2xy
As professor said the correct formula is
(10,000)(1+3/200)^2 - 10,000 = x (1+5/400)^4 - x
Applying the above trick we get:
10000(1 + 6/200)-10000 = x(1+5/100)-x
300 = 5x/100
x = 6000 approx.
SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008