Question

you want to study at the hogwarts school of witchcraft and wizardry after five years. you need 800 pieces of muggle - money to study there. you decide to deposit some pieces in the bank at a simple annual interest rate of 12%. how many pieces should you deposit today if you want to use the total amount to pay the fees? square pieces

Explanation:

Step1: Recall simple interest formula

The total amount \( A \) with simple interest is \( A = P(1 + rt) \), where \( P \) is principal (initial deposit), \( r \) is annual interest rate, \( t \) is time in years.

Step2: Rearrange to solve for \( P \)

\( P = \frac{A}{1 + rt} \)

Step3: Substitute given values

\( A = 800 \), \( r = 0.12 \), \( t = 5 \)
\( 1 + rt = 1 + (0.12 \times 5) = 1 + 0.6 = 1.6 \)
\( P = \frac{800}{1.6} \)

Step4: Calculate the principal

\( P = 500 \)

Answer:

500 pieces