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Jim invested $250 when he was 18 years old. His investment earned 8.5% interest compounded quarterly. How much would his investment be worth when he is 65?

User Anantha
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1 Answer

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Final answer:

Jim's investment of $250 at an 8.5% interest rate, compounded quarterly, will grow to approximately $6797.25 over 47 years by the time he is 65.

Step-by-step explanation:

To calculate the future value of Jim's investment, which earned 8.5% interest compounded quarterly, we use the compound interest formula:

A = P(1 + rac{r}{n})^{nt}

Where:

  • A = the amount of money accumulated after n years, including interest.
  • P = the principal amount (the initial amount of money).
  • r = the annual interest rate (decimal).
  • n = the number of times that interest is compounded per year.
  • t = the time the money is invested for, in years.

Jim invested $250 at an annual interest rate of 8.5%, compounded quarterly for a period from age 18 to 65, which is 65 - 18 = 47 years.

So our values are:

  • P = $250
  • r = 8.5% or 0.085
  • n = 4 (since the interest is compounded quarterly)
  • t = 47 years

Now we will plug these values into the formula:

A = 250(1 + rac{0.085}{4})^{4*47}

By calculating the value inside the brackets first and then raising it to the power of 188 (which is 4 times 47 years), we can find the total value of Jim's investment when he turns 65.

After doing the calculations:

A = 250(1 + rac{0.085}{4})^{188} = 250(1 + 0.02125)^{188}

A ≈ 250(2.7189)

A ≈ $6797.25

Jim's investment will be worth approximately $6797.25 when he is 65 years old, showing the power of compound interest over time.

User Mhopeng
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