anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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dumbcow
  • dumbcow
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
anonymous
  • anonymous
THANK YOU SO MUCH!

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