Question

A deferred annuity is a type of decreasing annuity whose term is to start at some future date. On his tenth birthday, a boy inherits $5,800, which is to be used for his college education. The money is deposited into a trust fund that will pay him R dollars on his 18th, 19th, 20th, and 21st birthdays. Find R if the money earns 10.5% interest compounded annually.

Answer 1

First find the balance on his 18th bday 8 years later
B = 5800*(1.105)^8 = 12,892.18
This is equal to the present value of all four payments of R
The present value can be written as:
PV = R(1+v+v^2+v^3)
where v = 1/1+i or v = 1/1.105
the sum of (1+v+v^2+v^3) is the sum of a geometric series
sum=1*(1-v^4)/(1-v)
put this together
12,892.18 = R*sum
R = 12,892.18/sum

hope that helps

Answer 2

THANK YOU SO MUCH!