a$.$ Assuming a rate of $10\%$ annually, find the FV of $$1,000$ after $5$ years.

b$.$ What is the investment's FV at rates of $0\%,5\%,$ and $20\%$ after $0,1,2,3,4,$ and $5$ years?

c$.$ Find the PV of $$1,000$ due in $5$ years if the discount rate is $10\%.$

d$.$ What is the rate of return on a security that costs $$1,000$ and returns $$2,000$ after $5$ years?

e$.$ Suppose California's population is $40$ million people and its population is expected to grow by $2\%$ annually. How long will it take for the population to double?

f$.$ Find the PV of an ordinary annulty that pays $$1,000$ each of the next $5$ years if the interest rate is $15\%.$ What is the annuity's FV$?$

g$.$ How will the PV and FV of the annuity in part $f$ change if it is an annuity due?

h$.$ What will the FV and the PV be for $$1,000$ due in $ years if the interest rate is $10\%,$ semiannual compounding?

i$.$ What will the annual payments be for an ordinary annuity for $10$ years with a PV of $$1,000$ if the interest rate is $8\%?$ What will the payments be if this is an annuity due?

f$.$ Find the PV and the FV of an investment that pays $8\%$ annually and makes the following end$-$of$-$year payments: