Deferred annuity S.Y.Tan

Deferred annuity - an annuity wherein the first payment interval does not coincide with the first interest period. The first payment is put off to some later date. Deferred annuity of n payments d+n d+(n-1) d+(n-2) d-1 d-2 2 1 R d d+1 d+2 1st payment starts on the (d+1)th period NO payment for d periods S.Y.Tan

Amount of a deferred annuity of n payments is equivalent to amount of an ordinary annuity of n payments. The present value of an annuity deferred for d periods is the value of the annuity or the value of the n payments in lump sum amount at the beginning of the term. Value of same annuity of n payments at one period before 1st payment date which is the end of d period Ordinary annuity of n payments translated for d periods Deferred annuity of n payments discount P for d periods d+n d+(n-1) d+(n-2) d-1 d-2 2 1 R d d+1 d+2 1st payment starts on the (d+1)th period NO payment for d periods d = period of deferment S.Y.Tan

Formula for the present value of an annuity of n payments deferred for d periods If the annuity is deferred by d periods, the first payment is then due at the end of the (d+1)th period. Similarly, if the 1st payment in due at the end of kth period, the period of deferment is always (k-1). S.Y.Tan

Ex 1 Find the present value of a P5,000 annuity payable quarterly for 7 years but deferred for 5 ½ years. Money is worth 9.6% converted quarterly. 50 49 48 21 20 2 1 5000 22 23 24 1st payment starts on the 23rd period period of deferment d = 22 Note: n = (last- first) + 1 28 = last – 23 + 1 Last = 28+23-1 = 50 S.Y.Tan

Ex 2 To start an IT business, Elmer and Erwin borrowed P4 Ex 2 To start an IT business, Elmer and Erwin borrowed P4.5M with interest at 10% compounded quarterly. They will repay the debt by making 12 equal quarterly payments. If the first payment is due at the end of 18 months, how much is the quarterly payment? 17 16 6 5 2 1 R 7 8 period of deferment d = 5 1st payment starts on the 6th quarter S.Y.Tan

EXERCISES Find the present value of a P50,000 annuity payable each three months for ten years but deferred for five years. Money is worth 12% compounded quarterly. On the birth of a child, the father wants to deposit a sum in a savings account. He intends to provide his daughter P20,000 every month for four years, starting on her 18th birthday. If the savings bank pays 10% compounded monthly, how much should the father deposit? A man borrowed P300,000 from a finance company that charges interest at 16% compounded semi-annually. He promised to pay off the loan in twelve semi-annual payments. The first payment is to be made at the end of two years. Find his semi-annual payment.

Ex Find the present value of a P50,000 annuity payable each three months for ten years but deferred for five years. Money is worth 12% compounded quarterly. 60 59 21 20 2 1 50000 22 23 period of deferment d = 20 1st payment starts on the 21st quarter S.Y.Tan

Ex On the birth of a child, the father wants to deposit a sum in a savings account. He intends to provide his daughter P20,000 every month for four years, starting on her 18th birthday. If the savings bank pays 10% compounded monthly, how much should the father deposit? 263 262 216 215 2 1 20000 217 218 period of deferment d = 215 1st payment starts on the 216th month S.Y.Tan

Ex A man borrowed P300,000 from a finance company that charges interest at 16% compounded semi-annually. He promised to pay off the loan in twelve semi-annual payments. The first payment is to be made at the end of two years. Find his semi-annual payment. 14 13 4 3 2 1 R 5 6 15 period of deferment d = 3 1st payment starts on the 4th period S.Y.Tan