Question

Voldemort has a savings account containing $\$10000$. interest accumulates so that every five years, the amount of money in that account grows to $\dfrac{11}{10}$ of its amount at the beginning of the five years. how much money is in that account after twenty years, given that no money is put into or taken out of the account?

Answer 1

Voldemort's savings account starts with $10,000 and grows to 11/10 of its amount every 5 years. After 20 years, the balance in the account, calculated using the formula for compound interest, will be $14,641.

Step-by-step explanation:

The question asks about the final amount in a savings account after 20 years with a specific interest accumulation pattern. To calculate the account balance after 20 years, given that the balance grows to 11/10 of its amount every 5 years, we can use the formula for compound interest. Voldemort starts with $10,000 and the balance increases by a factor of 11/10 every 5 years. Therefore, after 20 years (which is 4 periods of 5 years), the balance in the account will be:

$10,000 × (11/10)^4

Let's calculate this step by step:

1. Multiply the initial amount by the growth factor: $10,000 × 11/10 = $11,000 after the first 5 years.
2. Repeat this process for each subsequent 5-year period:

• 
  
• After 10 years: $11,000 × 11/10 = $12,100
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• After 15 years: $12,100 × 11/10 = $13,310
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• After 20 years: $13,310 × 11/10 = $14,641

Thus, after 20 years, the amount of money in the account will be $14,641.