Question

Assume you have a future liability of $16,000 per year for four years beginning six years from today. You will fund this liability over the next five years, with the first deposit to occur one year from today. If you earn 5% on this account annually, how much will you have to deposit at the end of each of the next five years to fund this liability?

Answer 1

Step 1:

Withdrawl amount = P = $16,000

n= 4 years

r = interest rate = 5%

Calculation of sum amount 5 years from today = P[ 1 - (1+r)^-n] / r

= $16,000 [1-(1+5%)^-4] / 5%

= $16,000 [1-0.82270247479] / 0.05

= $2,836.7604 / 0.05

= $56,735.2080666

Future value of sum of amount 5 years from today = $56,735.21

Step 2:

Annual Deposit Amount = P

n= 5 years

r = interest rate = 5%

Future value 5 years from today = $56,735.21

Future value = P * [((1+r)^n) - 1] / r

$56,735.21 = P * [((1+5%)^5) - 1] / 5%

$56,735.21 = P * [1.2762815625 - 1] / 0.05

$2,836.7605 = P * 0.2762815625

P = $10,267.6431765

Therefore, Annual Deposit Amount at the end of year for 5 years= $10,267.64