you want to study at the hogwarts school of witchcraft and wizardry after three years. you need 910 pieces…

you want to study at the hogwarts school of witchcraft and wizardry after three years. you need 910 pieces of muggle - money to study there. you decide to deposit some pieces in the bank at an annual interest rate of 10%. how many pieces should you deposit today if you want to use the total amount to pay the fees?

you want to study at the hogwarts school of witchcraft and wizardry after three years. you need 910 pieces of muggle - money to study there. you decide to deposit some pieces in the bank at an annual interest rate of 10%. how many pieces should you deposit today if you want to use the total amount to pay the fees?

Answer

Explanation:

Step1: Recall compound - interest formula for present value

The compound - interest formula for present value $PV$ when the future value $FV$ is known is $PV=\frac{FV}{(1 + r)^n}$, where $r$ is the annual interest rate and $n$ is the number of years.

Step2: Identify the values of $FV$, $r$, and $n$

We have $FV = 910$, $r=0.1$ (since $10%=0.1$), and $n = 3$.

Step3: Substitute the values into the formula

$PV=\frac{910}{(1 + 0.1)^3}=\frac{910}{1.1^3}=\frac{910}{1.331}$.

Step4: Calculate the present value

$PV=\frac{910}{1.331}\approx683.696469$. Rounding to the nearest whole - number, $PV = 684$.

Answer:

684