Question

he 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 $13.61 million to the The Wrist exactly 13 years from today. The team plans to make equal annual deposits into an account that will earn 5.5 percent in order to fund the payment. How much must the team deposit each year?

Multiple Choice

• $1,492,802.76

• $1,046,923.08

• $744,252.76

• $1,530,015.40

• $705,452.85

Answer 1

Option (c) is correct

Here, the deposits will be same every year, so it is an annuity. The future value of annuity is $13610000. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity = $13610000, P is the periodical amount, r is the rate of interest = 5.5% and n is the time period = 13

Now, putting these values in the above formula, we get,

$13610000 = P * ((1 + 5.5%)13 - 1 / 5.5%)

$13610000 = P * ((1 + 0.055)13 - 1 / 0.055)

$13610000 = P * ((1.055)13 - 1 / 0.055)

$13610000 = P * ((2.00577389748 - 1 / 0.055)

$13610000 = P * (1.00577389748 / 0.055)

$13610000 = P * 18.2867981359

P = $13610000 / 18.2867981359

P = $744252.76

So, the amount of money that we need to deposit each year is $744252.76