The president of a growing engineering firm wishes to give each of 50 employees a holiday bonusses. How much is needed to invest monthly for a year al 12% nominal rate compounded monthly, so that each employee will receive a P1,000 00 bonus?
To calculate the monthly investment needed, we can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)
Where:
FV = Future Value (total amount needed to be invested)
P = Monthly investment
r = Nominal interest rate
n = Number of compounding periods per year
t = Number of years
Given:
FV = 50 employees * P1,000.00 per employee = P50,000.00
r = 12% nominal rate = 0.12
n = 12 (compounded monthly)
t = 1 year
Plugging in the values:
50,000 = P * ((1 + 0.12/12)^(12*1) - 1) / (0.12/12)
Simplifying:
50,000 = P * ((1 + 0.01)^(12) - 1) / (0.01)
50,000 = P * (1.1268250301 - 1) / 0.01
50,000 = P * 0.1268250301 / 0.01
50,000 = 12.68250301P
Dividing both sides by 12.68250301:
P = 50,000 / 12.68250301
P ≈ 3,949.76
Therefore, the engineering firm needs to invest approximately P3,949.76 per month for a year at a 12% nominal rate compounded monthly to provide each employee with a P1,000.00 bonus.