Where a numerical answer is required, enter your answer as number

only. Do not include any currency symbols.

All answers must be correct to two places of decimal.

a$)$ Jennifer's lawyer estimates that she will receive $970,000$ if her

compensation claim succeeds. However, she will have to wait for $7$ years to

receive the money, if the case goes to court. Although Jennifer has a very

strong case, taking the risk of not winning into account, the appropriate

discount rate is $16\mathrm{.}8\%$ p$.$a$.$ What is the present value of this sum? $$

$(5$ Marks$)$

b$)$ Suppose, instead she settled the case for $14\%$ of the $970,000$ each

year, for the next $7$ years, with the first payment next year. As the case has

been settled, the appropriate discount rate would now be lower at $8\mathrm{.}4\%$

p$.$a$.$ what is the present value of this sum? $$

$(5$ Marks$)$

c$)$ Suppose instead Jennifer settled for a fixed monthly allowance of

$9,700$ for the next $7$ years $(84$ months$)$ starting next month. Again the

appropriate discount rate would be $8\mathrm{.}4\%$ p$.$a$.,$ how much would she receive

in present value terms? Clearly Show Your Workings. $$

Marks$)$

d$)$ Suppose Jennifer instead settled for a fixed monthly allowance of

$9,700$ for the next $7$ years $(84$ months$)$ starting today. The appropriate

discount rate would be $8\mathrm{.}4\%$ p$.$a$.$

i$)$ How much would she receive in present value terms? $$

$(7$ Marks$)$

ii$)$ If a friend offered to give her $650,000\mathrm{.}00,$ today in exchange for

the revenue stream from the fixed monthly allowance should she accept

this buyout offer?

$(2$ Marks$)$

e$)$ Finally, suppose that Jennifer, concerned about her childrens' future

welfare, opted to receive a monthly allowance that grew at $0\mathrm{.}5\%$ a month in

perpetuity starting next month. If all these future payments added together

were worth exactly $776,000$ in today's money terms and the appropriate

discount rate would be $1\mathrm{.}4\%$ per month, how much would she receive next

month? $$

$(9$ Marks$)$