Question

The terms of a single parent's will indicate that a child will receive an ordinary annuity of $12,000 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 10th birthday, how much money must be removed from the estate to purchase the annuity? (Assume an interest rate of 5%, compounded annually. Round your answer to the nearest cent.)

Answer 1

This can be found out using the Present value of annuity formula Present value of annuity is =P*(1-(1-1)^-n)/ Present value of annuity is = Money as on year 18 beginning "P" is Annual Payments =$ 12,000/- "r" is Rate of interest = 5% "n" is No of years = 7 years Present value of annuity is = 12000*(1-(1+0.05)^-7)/0.05 Present value of annuity is = 12000*0.28931867/0.05) Present value of annuity is = 12000*5.786373397 Present value of annuity is = 69,436.48/. The above present value is on 18th year beginning, we need to arrive at the amount to be depoisted on 10th birthday. So we need to compute the present value of $ 69,436.48 at 5% for 8 years before at 10th birthday Present value = Future value(1+r)^n Present value = (69436.48/(1+0.05)48) Present value = (69436.48/1.477455444) Present value = $ 46,997.347. Answer is $ 46,997.34).