Question

A new employee has decided to start saving $200 per month for the next five years. The employee uses a 6 percent per year compounded monthly interest rate for his planning.

a) What would be the present value (at time zero) of the five years of savings
b) When will the new employee have $4000 saved?

Answer 1

a). Calculate the Present Value of 5 years saving using Present Value of Ordinary Annuity:-

Where, C= Periodic Savings = $200

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods = 5 years*12 = 60

Present Value = $10,345.11

b). Calculating the time when Employee will have $4000 saved:-

Where, C= Periodic Savings = $200

r = Periodic Interest rate = 6%/12 = 0.5%

n= no of periods

Future Value = $4000

Taking Log on both sides,

Log(1.10) = n*Log(1.005)

0.041392685 =n*0.00216606

n = 19.11 months

So, Employee will save $4000 after 19 months