Show all keystrokes $($PV$,$ FV$,$ I$/$Y$,$ & N$)$ or formula to receive full credit for correct answers and for partial credit on problems you may not get $100\%$ correct $($final answers without any keystrokes or formula or calculation will receive $0$credit$).$

$1.$ What is the difference between nominal and effective interest rate?

$2.$ If you invest $$15,500$ at $5\mathrm{.}5\%$ interest, how much will you have in $2$ years?

$3.$ How much must you invest at $7\mathrm{.}5\%$ interest in order to see your investment grow to $$5,000$ in $5$ years?

$4.$ If Immanuel expects the investment to increase in value at a rate of $4\mathrm{.}5\%$ compounded annually for the next year. What is the effective interest rate?

$($Please use four decimals$)$

$5.$ What is the effective rate of return of a nominal interest rate of $4\mathrm{.}5\%$ compounded semiannually?

$($Please use four decimals$)$

$6.$ What is the effective rate of return of a nominal interest rate of $4\mathrm{.}5\%$ compounded quarterly?

$($Please use four decimals$)$

$7.$ What is the effective rate of return of a nominal interest rate of $4\mathrm{.}5\%$ compounded daily?

$($Please use four decimals$)$

$8.$ What would be the value of a savings account started with $$11,000$ earning $4\mathrm{.}5$ percent $($compounded annually$)$ after $6$ years?

$9.$ What would be the value of a savings account started with $$4,780,$ earning $8\mathrm{.}5$ percent $($compounded annually$)$ after $10$ years?

$($For questions $13-16).$ How much would you have to invest today to receive

$10.$ $$26,000$ in $8$ years at $11$ percent compounded semiannually

$11.$ $$36,000$ in $12$ years at $11$ percent compounded quarterly

$12.$ $$46,000$ in $13$ years at $11$ percent compounded monthly

$13.$ $$56,000$ in $15$ years at $11$ percent compounded daily

$($For questions $17-20).$ If you invest $$21,900$ today, how much will you have

$14.$ In $3$ years at $8\%?$

$15.$ In $7$ years at $9\%?$

$16.$ In $20$ years at $10\%?$

$17.$ In $60$ years $11\%?$

$18.$ How long will it take to double your money at $8\mathrm{.}5\%$ interest compounded annually?