How much money should be deposited in a bank for half a year at an interest rate of 4% p.a. in order to gain $5 000 simple interest?

To solve this problem, we need to use the formula for simple interest which is:

I = PRT

where: I = Interest P = Principal amount (the initial amount of money) R = Rate of interest T = Time the money is invested for

We know the Interest (I) is $5000, the Rate of interest (R) is 4% per annum (or 0.04 when expressed as a decimal), and the Time (T) is half a year (or 0.5 when expressed as a decimal). We want to find the Principal amount (P).

Rearranging the formula to solve for P gives us:

P = I / (RT)

Substituting the known values into the formula gives us:

P = 5000 / (0.04 * 0.5)

Calculating the above expression gives us the Principal amount (P) that should be deposited in the bank.