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What is the desired accumulated amount after 14 years invested in an account with 6.7% interest compounded monthly?

A. $20,000
B. $30,000
C. $40,000
D. $50,000

1 Answer

6 votes

Final answer:

To find out how much you need to deposit initially to achieve a future amount with compound interest, you can manipulate the compound interest formula. By applying this to an example with a 10% annual interest rate and a $10,000 target in ten years, you would need an initial deposit of approximately $3,855.43.

Step-by-step explanation:

To determine the initial deposit required to achieve a certain future value with compound interest, we can use the compound interest formula:

A = P (1 + r/n)(nt)

where:

  • A = the future value of the investment/loan, including interest.
  • P = the principal investment amount (initial deposit or loan amount).
  • r = the annual interest rate (decimal).
  • n = the number of times that interest is compounded per year.
  • t = the number of years the money is invested or borrowed for.

To solve for the principal P, we rearrange the formula:

P = A / (1 + r/n)(nt)

Using an example, if you want to have $10,000 in ten years in an account that pays 10% interest compounded annually, you would calculate:

P = $10,000 / (1 + 0.10/1)(1*10)

P = $10,000 / (1.10)10 ≈ $3,855.43

This demonstrates the power of starting to save early and allowing compound interest to work in your favor.

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