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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 910910 pieces of muggle-money to study there. You decide to deposit some pieces in the bank at an annual interest rate of 10% 10 \% .\newlineHow many pieces should you deposit today if you want to use the total amount to pay the fees?

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Q. You want to study at the Hogwarts School of Witchcraft and Wizardry after three years. You need 910910 pieces of muggle-money to study there. You decide to deposit some pieces in the bank at an annual interest rate of 10% 10 \% .\newlineHow many pieces should you deposit today if you want to use the total amount to pay the fees?
  1. Identify Variables: Identify the variables for the formula to calculate the present value.\newlineWe have:\newlineFuture Value (FV) = 910910 pieces of muggle-money\newlineNumber of years (nn) = 33\newlineAnnual interest rate (rr) = 10%10\% or 0.100.10\newlineWe need to find the Present Value (PVPV), which is the amount of money you need to deposit today.
  2. Use Formula: Use the formula for the present value of a single future amount.\newlineThe formula is:\newlinePV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}\newlineWe will use this formula to calculate how much money should be deposited today.
  3. Plug Values: Plug the values into the formula and calculate the present value.\newlinePV=910(1+0.10)3PV = \frac{910}{(1 + 0.10)^3}\newlinePV=910(1.10)3PV = \frac{910}{(1.10)^3}\newlinePV=9101.331PV = \frac{910}{1.331}\newlinePV≈683.92PV \approx 683.92
  4. Check Calculation: Check the calculation for any mathematical errors.\newlineRe-evaluate the exponent to ensure accuracy:\newline(1.10)3=1.10×1.10×1.10=1.331(1.10)^3 = 1.10 \times 1.10 \times 1.10 = 1.331\newlineNow, divide the future value by this result:\newlinePV=9101.331≈683.92PV = \frac{910}{1.331} \approx 683.92\newlineThe calculation appears to be correct.

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