Select the Correct Answer $($show all your work$)$

$1.$ At what rate must $$400$ be compounded annually for it to grow to $$855$ in $10$ years?

a$)6$ percent b$)5$ percent c$)7$ percent d$)8$ percent

$2.$ You wish to borrow $$4,000$ to be repaid in $12$ monthly installments of $$364\mathrm{.}12.$ The annual interest rate is:

a$)1$ percent b$)6$ percent c$)17$ percent d$)19$ percent.

$3.$ A commercial bank will loan you $$12,500$ for three years to buy a used car. The loan must be repaid in $36$ equal monthly payments. The annual interest rate on the loan is $6$ percent of the unpaid balance. How large are the monthly payments?

a$)$ $$380\mathrm{.}27$ b$)$ $$345\mathrm{.}53$ c$)$ $$372\mathrm{.}45$ d$)$ $$353\mathrm{.}05$

$4.$ If you put $$1850$ in a savings account with a $4\%$ nominal rate of interest compounded quarterly, what will the investment be worth in $21$ months $($round to the nearest dollar$)?$ a$)$ $$1867\mathrm{.}59$ b$)$ $$1956\mathrm{.}12$ c$)$ $$2045\mathrm{.}23$ d$)$ $$2,176\mathrm{.}45$