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).