Question

The terms of a single parent's will indicate that a child will receive an ordinary annuity of $17,000 per year from age 18 to age 24 (so that the child can attend college) and that the balance of the estate goes to a niece. If the parent dies on the child's 15th birthday, how much money must be removed from the estate to purchase the annuity? (Assume an interest rate of 8%, compounded annually. Round your answer to the nearest cent.) $

Answer 1

Answer:

  $75,881.59

Step-by-step explanation:

The value of the fund on the child's 17th birthday can be found from the amortization formula using r=.08 and t=7.

  17000 = Pr/(1 -(1+r)^-t) = P(.08)/(1 -1.08^-7) = 0.1920724P

  P = 17000/0.1920724 ≈ 88,508.29

There are 2 years between the 15th birthday and the 17th birthday, so the initial fund earns 8% interest for that time. It is multiplied by 1.08^2 to get the above value. The initial fund is then ...

  88,508.29 = 1.08^2 × initial fund

  initial fund = 88,508.29/1.08^2 ≈ 75,881.59

The amount of $75,881.59 must be used to purchase the annuity required to fund the payments to the niece.