Final answer:
You should invest approximately P 39,156.55 to have P 50,000 in 5 years at a 5% compounded annual interest rate, with the closest option being P 40,000 (option a).
Step-by-step explanation:
To calculate how much you should invest now to have P 50,000 in 5 years with an interest rate of 5% compounded annually, you would use the formula for compound interest: P = A / (1 + r)^n, where P is the principal amount (initial investment), A is the amount of money you want after n years, r is the interest rate per period, and n is the number of periods.
In this case, A is P 50,000, r is 0.05 (5% expressed as a decimal), and n is 5 years. Plugging these values into the formula gives us P = P 50,000 / (1 + 0.05)^5.
Calculating the denominator, we have (1 + 0.05)^5 = 1.27628. Then, dividing P 50,000 by 1.27628 gives us approximately P 39,156.55.
Therefore, the initial investment required to have P 50,000 in 5 years at a 5% interest rate compounded annually would be closest to P 40,000, which is option a). P 40,000