Problem

An investment company pays $9 \%$ compounded semiannually. You want to have $\$ 14,000$ in the future. (A) How much should you déposit now to have that amount 5 years from now?

Solution

Step 1 :Given that the future amount (A) is $14,000, the annual interest rate (r) is 9% or 0.09 in decimal, the number of times the interest is compounded per year (n) is 2 (since it's compounded semiannually), and the time the money is invested for (t) is 5 years.

Step 2 :We need to find the principal amount (P) that should be deposited now.

Step 3 :The formula for compound interest is \(A = P (1 + r/n)^{nt}\).

Step 4 :We can rearrange the formula to solve for P: \(P = A / (1 + r/n)^{nt}\).

Step 5 :Substituting the given values into the formula, we get \(P = 14000 / (1 + 0.09/2)^{2*5}\).

Step 6 :Solving the equation, we find that \(P \approx 9014.99\).

Step 7 :Therefore, you should deposit approximately \(\boxed{9014.99}\) now to have $14,000 in 5 years.

From Solvely APP
Source: https://solvelyapp.com/problems/39772/

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