Question

How much money should be deposited today in an account that earns 3% compounded semiannually so that it will accumulate to $10,000 in three years? Click the icon to view some finance formulas. The amount of money that should be deposited is $ (Round up to the nearest cent.)

Answer 1

To accumulate $10,000 in three years in an account that earns 3% compounded semiannually, you should deposit $9,254.26 today.

Step-by-step explanation:

To find the amount of money that should be deposited today in an account that earns 3% compounded semiannually so that it will accumulate to $10,000 in three years, we can use the formula for compound interest:

`P = A / (1 + r/n)^(n*t)`

Where P is the principal amount, A is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we want to solve for P:

`P = 10,000 / (1 + 0.03/2)^(2*3)`

This gives us a principal amount of $9,254.26. Therefore, the amount of money that should be deposited today is $9,254.26.