Find the present value of $20$ annual payments of $$1,000$ per annum where the first payment is

made $14$ years from now. So there are $20$ annual payments from $t=14$ to $t=33$ inclusive. The

discount rate is $22\%$ pa$.$ The present value of these payments is:

Select one:

a$.$ $$336\mathrm{.}27$

b$.$ $$342\mathrm{.}29$

c$.$ $$4,460\mathrm{.}27$

d$.$ $$4,540\mathrm{.}19$

e$.$ $$4,545\mathrm{.}45$

It's the first day of the year and you currently have $$4,000$ in the bank. You plan to deposit $$500$

at the end of every year for the next $52$ years, with the first payment made $1$ year from now

$($payments from $t=1$ to $t=52$ inclusive$).$

If bank interest rates are $9\%pa,$ how much money will be in your bank account a moment after

making your last deposit in $52$ years?

Select one:

a$.$ $$914,098\mathrm{.}05$

b$.$ $$838,622\mathrm{.}07$

c$.$ $$769,378\mathrm{.}04$

d$.$ $$379,376\mathrm{.}68$

e$.$ $$358,869\mathrm{.}35$