13. Harry Potter was very impressed with the education he received at Hogwarts.

Question

13. Harry Potter was very impressed with the education he received at Hogwarts. He would like to give them a meaningful gift, but doesn't have a lot of money right now, fighting evil wizards and new wands has drained his bank account. He decides that he will open a new account at Gringotts for this purpose. Gringotts has promised to pay him 9% interest compounded annually. Harry will leave this gift to Hogwart's upon his death. Assuming that he lives another 70 years, deposits $ 1,440 in the account today, and the account earns 9% interest per year, how much will Hogwart's get in 70 years? (rounded to the nearest 1,000) a. $1,000,000 b. $67,000 c. $187,000 d. $600,000

Explanation / Answer

Formula for compound interest:

A = P x (1+i/n)t

Where,
   P = principle amount = $ 1,440

   A = Amount after maturity
   i = Interest rate = 9 % or 0.09 p.a.

   n = No. of compounding frequency in a year = 1
   t = number of periods = 70

A = $ 1,440 x (1 + 0.09)70

   = $ 1,440 x (1.09)70

   = $ 1,440 x 416.7300862

   = $ 600,091.3241 or $ 600,000    [on rounding to nearest 1000]

Hence option “d. $ 600,000” is correct answer.

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