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!
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!
Answer
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.
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 )
