Question

What lump sum of money must be deposited into a bank account at the present time so that

​$550 per month can be withdrawn for four years, with the first withdrawal scheduled for

five years from​ today? The interest rate is 3​/4​%

per month.​ (Hint: Monthly withdrawals begin at the end of the month

60​.)

Answer 1

Step 1

Find out the present value of $550 per month withdrawal at the end of 5th year

We can use present value of annuity formula.

Present value of annuity = P x {[1-(1+r)^-n] / r}

Present value of annuity = Present value of $550 per month withdrawal at the end of 5th year = ?

P = monthly withdrawal = $550

r = rate of interest per month = 0.0075

n = no.of months = 4 years * 12 = 48

Present value of annuity = 550 x {[1-(1+0.0075)^-48] / 0.0075}

Present value of annuity = 550 x 40.18478

Present value of annuity = 22101.63

Present value of $550 per month withdrawal at the end of Month 60 = $22,101.63

Step 2

Find out the present value of $22101.63 in present terms.

The lump sum of money must be deposited into a bank account at the present time = Present value of $550 per month withdrawal at the end of Month 60 x discount factor of 60th Month

The lump sum of money must be deposited into a bank account at the present time = 22101.63 x [1/1.0075^60]

The lump sum of money must be deposited into a bank account at the present time = $14,116.30