anualidades continuas

231

25 CONTINUOUS ANNUITIES 

Practice Pract ice Proble Problems ms Problem 25.1

Calculate the present value of a continuous annuity of 1,000 per annum for 8 years at: (a) An annual effective interest rate of 4%; (b) A constant force of interest of 4%. Problem 25.2

Find the force of interest at which s20 = 3s10 . Problem 25.3

If  an  = 4 and sn = 12, find δ. Problem 25.4

There is $40,000 in a fund which There which is accum accumulatin ulatingg at 4% per p er annum converti convertible ble continuou continuously sly.. If  money is withdrawn continuously at the rate of $2,400 per annum, how long will the fund last? Problem 25.5

Annuity A   offers to pay you $100 per annum, convertible continuously, for the next five years. Annuity B  offers you $ X at the end of each year for ten years. The annual effective interest rate i is 8%. Find X  such that you are indifferent between the two annuities. Problem 25.6

Given δ  =  = 0.1.  Evaluate

a

(12)

10 a 10

.

Problem 25.7

You are given

d s dt t

= (1.02)2t .  Calculate δ.

Problem 25.8

Given an =  n − 4 and δ  =   = 10%,  find

  n 0

at dt.

Problem 25.9

Payment Payme ntss wil willl be mad madee to you at a con contin tinuou uouss rat ratee of $100 per year for the nex nextt fiv fivee ye years ars.. The effective rate of interest over this period is i = 0.06.  Calculate the present value of this payment stream. Problem 25.10

Show that

d a dt t

=

ν t s 1

.

232

THE BASICS OF ANNUITY THEORY 

Problem 25.11 (m)

Show that an < an

(m)

< an <  ¨ an

<  ¨an .  Hint: See Example 10.15.

Problem 25.12

Find an expression for t, 0  < t