# A Financial Math Question

Question

The amount of interest earned on \$K for one year is \$256.
The amount of discount paid on a one year loan “for \$K,” transacted on a discounted basis at a discount rate that is equivalent to the interest rate of the first transaction, is \$236.
Find \$K!
Firstly, when it is not stated in a problem whether its “simple interest” or “compound interest”, you “always” assume compound interest. Why? It’s just convention. Let i = interest and d = discount rate = i / ( 1 + i ) by definition. “the amount of interest earned on \$K for one year is \$256.”
So, Ki = 256.

“The amount of discount paid on a one year loan “for \$K,” transacted on a discounted basis at a discount rate that is equivalent to the interest rate of the first transaction, is \$236″
means,
dK = 236.
That is since d = i / ( 1+ i),
(iK) / ( 1+ i ) = 236
But iK = 256 from above, so…
(256)/( 1 + i ) = 236,
1 + i = 256/236 = 1.0847,
i = 0.0847 or 8.47%

Hence K = 256/i = 256/0.0847 = \$ 3022.43 ( approximately )