Question

You will start to set aside money at the end of this month to fund a capital project at a rate of 50,000 per month until the project is finished. At the start of the project, costs will be 150,000 per month for the 24-month duration of the project. If you already have 250,000 saved, what is the minimum number of months you will need to continue saving before you may start the project if interest is 18% nominal, compounded monthly?

Answer 1

Amount to be saved at end of each month = $50000

Let the number of months be n

Interest rate = 18% /12 monthly = 0.18/12

FV of the investments after n months = 250000(1+0.18/12)ⁿ + 50000[(1+0.18/12)ⁿ -1]/(0.18/12)

Value of the cost outflows at time period n = 150000[1 - (1+0.18/12)^-24]/(0.18/12) = 3004560.80

Hence, 250000(1+0.18/12)ⁿ + 50000[(1+0.18/12)ⁿ -1]/(0.18/12) = 3004560.80

=> 3583333.33(1+0.18/12)ⁿ = 6337894.13

=> n = 43.17 months

Hence savings of 50000 needs to be done for minimum of 44 months