A newspaper editor starts a retirement savings plan, depositing $225 per month at the beginning of each month into an account that earns an annual interest rate of 6.8% compounded monthly. Find the value of the interest in dollars after 20 years. Round your answer to the nearest cent.

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Answer :

malikmemoona395 malikmemoona395 · Answer 1 · 2024-10-22T01:21:02-04:00

Final Answer:

After 20 years, the value of the retirement savings plan will be approximately $88,460.40.

Explanation:

To calculate the future value of the retirement savings plan, we can use the formula for compound interest:

[tex]\[A = P \left(1 + \frac{r}{n}\right)^{nt}\][/tex]

Where:

- [tex]$A$[/tex] is the future value of the investment/loan, which we want to find.

[tex](P\)[/tex] is the principal amount, which is $225 in this case (the monthly deposit).

- [tex]$r$[/tex] is the annual interest rate, which is 6.8% or 0.068 in decimal form.

- [tex]$n$[/tex] is the number of times that interest is compounded per year, which is 12 times monthly.

-[tex]$t$[/tex]is the number of years the money is invested for, which is 20 years.

Now, we can plug these values into the formula:

[tex]\[A = 225 \left(1 + \frac{0.068}{12}\right)^{(12 \times 20)}\][/tex]

Solving this equation gives us the future value:

[tex]\[A \approx 88460.40\][/tex]

So, after 20 years, the retirement savings plan will be worth approximately $88,460.40.

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