Question

You have decided to start your own firm. Being prudent, you want to have enough money saved to use for living expenses for two years before you quit. You can currently put away $45,000 a year. You know that you will have living expenses of $75,000 a year for each of the two years (paid at the end of the year, simplifying assumption). You would like to quit in three years. If you put $45,000 into an account bearing 5% interest each of the next two years, how much must you put into the account at the end of Year 3 so that you can quit?

Answer 1

FV of Annuity = P*[{(1+i)^n}-1]/i

Where, P = Annuity = 45000, i = Interest Rate = 0.05, n = Number of Periods = 3

Therefore, FV = 45000*[{(1+0.05)^3}-1]/0.05 = 45000*0.157625/0.05 = $141862.5

Note: As, FV at the end of 3rd year is required, we will calculate FV of Annuity for 3 years and the subtract the last installment, because actual deposit is to be made for only 2 years.

FV of $45000 deposited for 2 years, at the end of 3rd year = FV of Annuity for 3 years - 3rd Deposit = 141862.5 - 45000 = $96862.5

Amount that should be in the account, that will be equivalent for cost of living of $75000 for next 2 years = PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, P = Annuity = 75000, i = Interest Rate = 0.05, n = Number of Periods = 2

PV = 75000*[1-{(1+0.05)^-2}]/0.05 = 75000*0.09297/0.05 = $139455.78

Amount to be kept in the account at the end of year 3 = 139455.78-96862.5 = $42593.28