A geometric perpetuity$-$due provides annual payments. The first payment is $1,$ and ea

subsequent payment is $2\%$ less than the previous payment. Let M be the price of this perpetuity

using an annual effective interest rate of $8\%.$

The price should have been calculated using an annual effective interest rate of $7\%.$ Let P be the

correct price of this perpetuity and let E be the estimate of P based on the initial price, M$,$ using

the first$-$order Macaulay approximation.

Calculate $($E$-$P$)/$P$,$ the percentage error of the estimate.

$($A$)1\mathrm{.}48\%$

$($B$)1\mathrm{.}16\%$

$($C$)0\mathrm{.}92\%$

$($D$)0\mathrm{.}49\%$

$($E$)0\mathrm{.}26\%$