Question

The terms of a single parent's will indicate that a child will receive an ordinary annuity of $20,000 per year from age 18 to age 24 (so the child can attend college) and that the balance of the estate goes to a niece. If the parent dies on the child's 17th birthday, how much money must be removed from the estate to purchase the annuity? (Assume an interest rate of 9%, compounded annually

Answer 1

Interest, i=9%=0.09 p.a.
Future value, S

Ordinary annuity for 6 years,
n=6
yearly payment, R = $20,000

Find future value when child will be 24 years old:
S = R((1+i)^n-1)/i
= $20,000*(1.09^6-1)/0.09
= $20,000*(7.523335)
= $150,466.69

Present value (when child is 17)
P= S/(1+i)^7
= $82310.43