In each case, determine the effective annual rate and the effective continuous rate.

$($a$)0\mathrm{.}6\%$ APR compounded monthly.

$($b$)1\mathrm{.}8\%$ APR compounded weekly.

$($c$)3\%$ APR compounded daily.

$($d$)0\mathrm{.}3\%$ APR compounded continuously.

$($e$)0\mathrm{.}6\%$ compounded monthly.

$($f$)1\mathrm{.}8\%$ compounded weekly.

$($g$)3\%$ compounded daily.

$2.$ Randall$$s saving accounts earns interest at $4\%$ APR, compounded on the first day of each month. He makes the

following deposits:

$$ October $4$th $2024$: $$100.$

$$ November $15$th $2024$: $$200.$

$$ February $20$th $2025$: $$300.$

Determine Randall$$s account balance as of March $31$st $2025.$

$3.$ Vince$$s saving accounts earns interest at $4\%$ APR, compounded continuously. He makes the following deposits:

$$ March $1$st $2024$: $$100.$

$$ June $1$st $2024$: $$200.$

$$ December $1$st $2025$: $$300.$

Determine Vince$$s account balance as of March $1$st $2025.$

$4.$ Two friends, Prunella and Sue Ellen, each open their own savings accounts on January $1$st$,2025.$ Prunella

deposits $$15$; her account grows at $1\mathrm{.}2\%$ APR, compounded bimonthly $($every two months$).$ Sue Ellen deposits

$$10$; her account grows at $0\mathrm{.}8\%$ APR, compounded weekly.

Will Sue Ellen$$s account balance ever exceed Prunella$$s$?$ If so$,$ determine the month and year in which Sue

Ellen$$s account balance first exceeds Prunella$$s$.$ If not, explain why.

$5.$ Theodore$$s savings account earns interest continuously. He makes the following deposits:

$$ January $1$st $2027$: $$200$

$$ January $1$st $2028$: $$300$

On January $1$st $2029,$ his account balance is exactly $$800.$ Determine the APR of Theodore$$s account.

$6.$ Gretchen invests a lump sum that grows at $1\mathrm{.}9\%$ APR, compounded daily. How long will it take for her investment

to triple?

$7.$ Ashley invests a lump sum that compounds interest every second week. After two$-$and$-$a$-$half years, her invest$-$

ment has grown by $65\%!$ Determine the APR on her investment.

$8.$ Mr$.$ Prickly intends to invest a lump sum that compounds interest continuously, at $1\mathrm{.}29\%$ APR. His goal is for

the balance to reach $$2000$ over the next seven months. How much money should Mr$.$ Prickly invest today?

$1$