Question

The Nashville Geetars , a professional foosball team , has just signed its star player Harold "The Wrist" Thornton to a new contract. One of the terms requires the team to make a lump sum payment of $13.31 million to the The Wrist exactly 10 years from today . The team plans to make equal annual deposits into an account that will earn 5.05 percent in order to fund the payment. How much must the team deposit each year?

Answer 1

Assume that the deposits are made at the beginning of each year.

The future value of money deposited today is,

= PV*(1+r)^t

Where,

PV is the money deposited today

r is the interest rate

t is time in years

So, the lump sum amount after 10 years is equal to sum of future values all the annual deposits.

13.31 = P(1+5.05/100)^10 + P(1+5.05/100)^9 + ..........+ P(1+5.05/100)^1

13.31 = P(1.0505)((1.0505^10) -1)/(1.0505 - 1)

P = 1.00498