Question

How much does Savannah need to save at the end of each of the next twenty-five years (with the first deposit made at the end of year 1) to have an income of $40,000 per year for thirty years starting at end of year twenty-six. The appropriate interest rate is 6.0% p.a.

Answer 1

From Year 26 to Year 56,

Annual Income = $40,000

Time Period = 30 years

Interest Rate = 6%

Calculating Present Value at the end of Year 25,

Present Value of Annuity = P[(1 - (1 + r)^-n)/r]

Present Value = 40000[(1 - (1.06)^-30)/0.06]

Present Value = $550,593.25

Now,

Using Present Value at year 25 as Future Value,

FV = $550,593.25

Time Period = 25 years

Interest Rate = 6%

Calculating Annual Deposit,

Using TVM Calculation,

PMT = [PV = 0, FV = 550,593.25, I = 0.06, T = 25]

PMT = $10,035.51

Annual Deposit = $10,035.51