An employee is about to receive the sum of P 300.00 at the end of each year for 5 years. One year prior to the receipt of the first sum, he decides to discount all 5 sums. If the interest rate is 6%, what proceeds will he obtain?
To find the present value of the 5 sums, we can use the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PMT = annuity payment (P 300.00)
r = interest rate (6% or 0.06)
n = number of periods (5)
Substituting the given values into the formula:
PV = P 300.00 * [(1 - (1 + 0.06)^-5) / 0.06]
Calculating inside the brackets:
PV = P 300.00 * [(1 - (1.06)^-5) / 0.06]
PV = P 300.00 * [(1 - 0.7473) / 0.06]
PV = P 300.00 * [0.2527 / 0.06]
PV = P 300.00 * 4.2117
PV = P 1263.51
Therefore, the employee will obtain P 1263.51 as the discounted proceeds for the 5 sums.