$5.$

$($a$)$ What effective force of interest per quarter$-$year is equivalent to an effective rate of interest of $16\%$ per two years?

$($b$)$ What effective rate of interest per $0\mathrm{.}9$ years is equivalent to an effective rate of interest of $1\mathrm{.}3\%$ per four months?

$($c$)$ Assume the effective rate of interest is $5\%$ p$.$a$.$ from $1$ January $2011$ to $31$ July $2011$ and it is $0\mathrm{.}8\%$ per month thereafter. An investor will receive $150,000\mathrm{.}00$ on $1$ May $2011$ and a further $120,000\mathrm{.}00$ on $1$ November $2011.$ What is the total accumulated value on $1$ January $2012$ of these cash flows? What is the present value of these cash flows on $1$ January $2011.$

$($d$)$ You are promised to receive a lump sum payment of $600,000\mathrm{.}00$ in $25$ years time. Calculate the purchasing power today of the $600,000\mathrm{.}00$ under the assumption that the average rate of inflation over the next $25$ years is

$($i$)3\%$ p$.$a$.$

$($ii$)5\%$ p$.$a$.$

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