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Samir is going to invest in an account paying an interest rate of 2.5% compounded daily. How much would Samir need to invest, to the nearest ten dollars, for the value of the account to reach $14,000 in 16 years?​

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Final answer:

To find out how much Samir needs to invest, we can use the formula for compound interest. Plugging in the given values, we find that Samir needs to invest approximately $7,010 (rounded to the nearest ten dollars) to have the value of the account reach $14,000 in 16 years.

Step-by-step explanation:

To find out how much Samir needs to invest, we can use the formula for compound interest.

The formula is A = P(1 + r/n)^(nt), where A is the future value of the investment, P is the initial principal (the amount to be invested), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the number of years.

In this case, Samir wants the value of the account to reach $14,000 in 16 years.

The interest rate is 2.5% compounded daily, which means n = 365 (since interest is compounded daily) and r = 0.025 (since the annual interest rate is 2.5%). We need to solve for P.

Plugging in the values into the formula, we have: 14000 = P(1 + 0.025/365)^(365*16)

Simplifying the equation, we get: P = 14000 / (1 + 0.025/365)^(365*16)

Using a calculator, we find that P is approximately $7,010 (rounded to the nearest ten dollars).

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