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?
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.
To calculate the interest Daria can expect to earn after 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (initial investment) = $3000
r = annual interest rate (as a decimal) = 9% = 0.09
n = number of times interest is compounded per year = 1 (compounded annually)
t = number of years = 10
Plugging in the values into the formula:
A = 3000(1 + 0.09/1)^(1*10)
Simplifying:
A = 3000(1 + 0.09)^10
A = 3000(1.09)^10
Using a calculator, we can find:
A ≈ $6336.05
To calculate the interest earned, we subtract the initial investment from the final amount:
Interest = A - P
Interest = $6336.05 - $3000
Interest ≈ $3336.05
Therefore, Daria can expect to earn approximately $3336.05 in interest after 10 years.
To calculate the interest Daria can expect to earn after 10 years on her investment, you need to use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of compounding periods per year
t = the number of years
Let's plug in the given values:
P = $3000
r = 9% or 0.09 (converted to decimal form)
n = 1 (since the interest is compounded annually)
t = 10 years
Using the formula, we have:
A = 3000(1 + 0.09/1)^(1*10) - 3000
Calculating further:
A = 3000(1.09)^10 - 3000
A = 3000(1.093742745) - 3000
A ≈ 3278.23 - 3000
A ≈ $278.23
Therefore, Daria can expect to earn approximately $278.23 in interest after 10 years on her $3000 investment in the mutual fund.