Mike wants to donate $$5,000,000$ to establish a fund to provide an annual scholarship in perpetuity. The fund will earn an interest rate of $4\mathrm{.}57\%$ p$.$a$.$ compounded half$-$yearly $($j$2=4\mathrm{.}57\%$ p$.$a$.)$ and the first scholarship will be first awarded $3\mathrm{.}5$ years after the date of the donation.

$($a$)$ What is the amount of the annual scholarship $($rounded to two decimal places$)?$

Question $9$ Answer

a$.$

$127913\mathrm{.}37$

b$.$

$255507\mathrm{.}69$

c$.$

$260410\mathrm{.}57$

d$.$

$258749\mathrm{.}57$

Mike wants to donate $$5,000,000$ to establish a fund to provide an annual scholarship in perpetuity. The fund will earn an interest rate of $4\mathrm{.}57\%$ p$.$a$.$ compounded half$-$yearly $($j$2=4\mathrm{.}57\%$ p$.$a$.)$ and the first scholarship will be first awarded $3\mathrm{.}5$ years after the date of the donation.

$($b$)$ Assume that two years after the donation, Mike needs to withdraw $$1,000,000$ from the fund and use the remaining amount to provide an annual scholarship in perpetuity. The time of the first scholarship will be unchanged $(3\mathrm{.}5$ years after the date of the donation$).$ What is the new annual scholarship amount $($rounded to two decimal places$)?$

Question $10$ Answer

a$.$

$211471\mathrm{.}27$

b$.$

$104541\mathrm{.}25$

c$.$

$208775\mathrm{.}11$

d$.$

$212853\mathrm{.}05$