$.$ Mr$.$ Graham is saving $$450,000$ per year in a savings account that is paying annual compound

interest of $3\%.$ He intends to continue this for three years after which he will move it to

JMMB$$s long term fund which pays interest of $8\%$ per annum compounded semi$-$annually.

i$.$ How much would he be able to transfer to JMMB after $3$ years? $(3$ marks$)$

ii$.$ How much money will he have at the end of $8$ years from today? $-3$

FV of an ordinary annuity due

$7.$ An annuity makes $25$ annual payments of $$1,000$ with the first payment coming today. What

is the future value of this as of $25$ years from now if the interest rate is $9\%?-3$