Answer to Question #281481 in Algebra for Ashley Bonete

Question

A.Find the period of deferral in each of the following deferred annuity problem (one

way to finnd the period of deferral is to count the number of artificial payments)

1.Monthly payments of P2,000 for 5 years that will start 7 months from now

2. Annual payments of P8,000 for 12 years that will start 5 years from now

3. Quarterly payments of P 5,000 for 8 years that will start two years from now.

4.Semi-annual payments of P60,000 for 3 years that will start 5 years from now

5.Payments of P3,000 every 2 years for 10 years starting at the end of 6 years

Answer 1

Period of deferral, $k$ is given by

$k=nt-1$

Where

$k=$ period of deferral

$n=$ Number of times compounded per year

$t=$ Time in year deferred

1)

$n=12\>\>t=\frac{7}{12}\>\>\\k=12(\frac{7}{12})-1=6\>periods$

2)

$n=1\>\>t=5\\ k=5-1=4\>years$

3)

$n=\frac{12}{3}=4\>\>\>t=2\>years\\k=2×4-1=7\>quarters$

4)

$n=\frac{12}{6}=2\>\>\>t=5\\k=5×2-1=9\>periods \>of \>half\> years$

5)

$n=\frac{1}{2}=0.5\>\>\>t=6\>years\\k=0.5×6-1=2\>periods$