DEFERRED ANNUITY -the first payment is made several periods after the beginning of the annuity Finding P given A: P 1 2 m 1 2 3 n-1 n _________________......________________________.......______ 0 A A A A A [---Deferment period------][-------------- n periods --------------------] P1 m 1 2 3 n-1 n ________________________.......______ A A A P1 = A{[1 – (1+i)-n] / i} P P1 1 2 3 _____|_____|_____|____.....__ m Recall: P = F(1+i)-n P = P1 (1+i)-m P = A{[1-(1+i)-n] / i} (1 + i)-m A A Finding F given A: The accumulated amount F is the same as that for an ordinary annuity. F = A {[(1 + i)n – 1] / i} Examples: 1. A man invests P10,000 now for the college education of his 2 year-old son. If the fund earns 14% annually, how much will the son get each year starting from his 18th to the 22nd birthday? 2. A lathe for a machine shop costs P60,000 if paid in cash. On the installment plan, a purchaser should pay P20,000 down payment and 10 quarterly installments, the first is due at the end of the first year after purchase. If interest rate is 15% compounded quarterly, determine the quarterly installment. 3. A person buys a piece of property for P100,000 down payment and 10 deferred semi-annual payments of P8,000 each starting three years from now. What is the present value of the investment if the rate of interest is 12% compounded semi-annually? 4. A new generator set has just been installed. It is expected that there will be no maintenance charges until the end of the 6th year, when P300 will be spent on the generator at the end of each successive year until the generator is scrapped at the end of the 14th year of service. What sum of money set aside at the time of installation of the generator at 6% interest will take care of all maintenance expenses for the generator? Answers: 1. A = P20,793.00 2. A = P5,439.16 3. P = 143,999.09 4. P = 1,392.09