Ms Maryanne to Is Seeking to Calculate the Amount of Life

Question

Examlex · Accepted Answer

The Answer is The annual amount required to Maryanne's financial dependants will be:

\$ 45,000 imes 80 \% = \$ 36,000

a) The life insurance cover required where payment are withdrawn on a monthly basis in arrears will be:

ext { Payment } = \frac { \$ 36,000 } { 12 } = \$ 3,000

Number of periods

= 25

years

\mathrm { x } 12 = 300

Rate per period

\quad = \frac { 6 \% } { 12 } = 0.5 \%

\begin{aligned}& P V = P M T \left[ 1 - ( 1 + i ) ^ { - n } ight] \= & \frac { \$ 3,000 \left[ 1 - ( 1 + 0.5 \% ) ^ { - 300 ] } ight. } { 0.5 \% } \= & \frac { \$ 3,000 ( 1 - 0.224 ) } { 0.5 \% } \= & \frac { \$ 2,328.103 } { 0.5 \% } \= & \$ 465,621\end{aligned}

In addition, Maryanne has specified that her financial dependants will also require

\$ 100,000

at the time of her death increasing the total life cover required to the amount of:

\$ 465,621 + \$ 100,000 = \$ 565,621

Rounding this amount off provides a required life cover amount of

\$ 566,000

. b) The life insurance cover required where payments are withdrawn on a six-monthly basis in arrears will be:

\begin{array} { l l } ext { Payment } = \frac { \$ 36,000 } { 2 } & = \$ 18,000 \\ ext { Number of periods } & = 25 ext { years } imes 2 = 50 \ ext { Rate per period } & = \frac { 6 \% } { 2 } = 3 \%\end{array}

\begin{aligned}& P V = P M T \left[ 1 - ( 1 + i ) ^ { - n } ight] \= & \frac { \$ 18,000 \left[ 1 - ( 1 + 3 \% ) ^ { - 50 ] } ight. } { 3 } \= & \frac { \$ 18,000 ( 1 - 0.228 ) } { 3 \% } \= & \frac { \$ 13,894.07 } { 3 \% } \= & \$ 463,136\end{aligned}

In addition, Maryanne has specified that her financial dependants will also require

\$ 100,000

at the time of her death increasing the total life cover required to the amount of:

\$ 463,136 + \$ 100,000 = \$ 563,136

Rounding this amount off provides a required life cover amount of

\$ 563,000

. c) The amount in part b) of the question ($563,000) is less than that for part a) ($566,000) due to the longer payment period (six-monthly rather than monthly). Applying time value of money principles, the longer the period that the dependants are willing to wait to receive their payments the relatively lower the present value given that the remaining capital amount will both be greater and have longer to accumulate for option b) (at the given discount rate - in this case 6% p.a.).

Ms Maryanne to Is Seeking to Calculate the Amount of Life

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