Question

If starting with x amount of money, and that money increases by 50% every day for y days, what formula determines the final amount of money after y days?

(A) ( x × (1 + 0.50)ʸ )
(B) ( x × (1 + 0.50y) )
(C) ( x × (1 + 0.50)ʸ/ (365 )
(D) ( x × (1 + y)⁰.50 )

Answer 1

The accurate formula to calculate the final amount of money after y days, when it increases by 50% daily, is (A) ( x × (1 + 0.50)ˢ ).

Step-by-step explanation:

If starting with x amount of money, and that money increases by 50% every day for y days, the formula that determines the final amount of money after y days is (A) ( x × (1 + 0.50)ˢ ). This is because the increase is compound in nature, similar to how compound interest is calculated in a bank account. Each day, the amount is multiplied by 1.50 to account for the 50% increase.

As an example, similar to a bank account bearing 2% annual interest where the money grows by 1.02 each year, if we apply a daily growth rate, we would multiply the original amount by (1 + interest rate) to the power of the number of periods, which in this case are days.