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.