An investor makes deposits into an account at the end of each year for ten years. The deposit in year one is $1,$ year two is $2$ and so

forth until the final deposit of $10$ in year ten. The account pays interest at an annual effective rate of $i.$

Immediately following the final deposit, the investor uses the entire account balance to purchase a perpetuity$-$immediate at an annual

effective interest rate of $i.$ The perpetuity makes annual payments of $10.$

Calculate the purchase price of the perpetuity.

$68\mathrm{.}0$

$72\mathrm{.}4$

$76\mathrm{.}2$

$81\mathrm{.}3$

$91\mathrm{.}3$