The present value of an annuity is
PV = Pmt x (1 - 1 / (1 + i)^n) / i
http://www.tvmschools.com/formula/presen...
For the first annuity
PV =1000 x (1 - 1 / (1 + 3%)^6) / 3%
PV = 5,417.19
For the second annuity
PV =1500 x (1 - 1 / (1 + 3%)^4) / 3%
PV = 5,575.65
But this is the value at the start of year 7 so needs discounting back 6 years using the present value of a lump sum formula
PV = FV / (1 + i)^n
http://www.tvmschools.com/formula/presen...
PV = 5575.65 / (1 + 3%)^6
PV = 4,669.52
Total PV = 5,417.19 + 4,669.52 = 10,086.71
This must be the same as the balance on the account today.
(Making up this question as I go)
Bob takes out $1,000 from his bank account every year for 6 years. Suddenly he had in increase his withdrawals by $500 every year. He now takes out $1,500 every year for 4 years until his account is empty. The interest rate is 3%. What did he initially have?
I know that you are supposed to use the present worth formula, but I can't seem to organize it so that it works.
Halp.
