Question

To calculate how much Mia's investment will be worth after a certain period of time with a guaranteed annual return, you can use the formula for compound interest:

A = P(1 + r/n)⁽ⁿᵗ⁾
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years the money is invested for
In Mia's case:
P (the initial investment) = $50,000
r (annual return rate) = 7% or 0.07 (as a decimal)
n (compounding frequency) is not specified, so we'll assume it's compounded annually, which is common.
t (the number of years) is not provided in the question, so we'll calculate the future value for different time periods.

Answer 1

To find the future value of Mia's investment, the compound interest formula is used with a principal of $50,000 and an annual interest rate of 0.07, compounded annually. Examples of different periods would show the growth of the investment due to compound interest.

Step-by-step explanation:

To calculate the future value of Mia's investment with a guaranteed annual return, we can use the compound interest formula: A = P(1 + r/n)^(nt). With a principal P of $50,000, an annual interest rate r of 0.07, and typical annual compounding (n = 1), we would substitute these values into the formula for various numbers of years, t, to get the total future amount. Compound interest differs from simple interest in that it applies not only to the principal but also to the accumulated interest from previous periods.

Example Calculation:

For a 5-year investment period, the calculation would be: A = 50,000(1 + 0.07/1)^(1*5) = 50,000(1.07)^5 ≈ $70,257.96, which shows the investment grows significantly more compared to the initial investment thanks to compound interest.