Question

Daria invests $3000 in a mutual fund. On average, the mural fund earns 9%/yr compounded annually. How much interest can Daria expect to earn after 10 years?

Answer 1

To calculate the interest earned on the investment, we can use the formula for compound interest:

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

Where:
A = the ending balance (including interest)
P = the principal investment
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

In this case, Daria's principal investment (P) is $3000, the annual interest rate (r) is 9%/yr or 0.09, the number of times interest is compounded per year (n) is 1 (compounded annually), and the number of years (t) is 10.

Plugging in the values, we have:

A = 3000(1 + 0.09/1)^(1*10)
A = 3000(1 + 0.09)^10
A = 3000(1.09)^10
A ≈ 3000(1.9477)
A ≈ $5843.10

To find the interest earned, we subtract the principal investment from the ending balance:

Interest = A - P
Interest = $5843.10 - $3000
Interest ≈ $2843.10

Therefore, Daria can expect to earn approximately $2843.10 in interest after 10 years.