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Q$1.$ You have been told that you need $$x$ today in order to have $$100,000$ when you retire $20$ years from now. The annual interest rate is $5\%$ on average. Compute $x.$

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Q$2.$ You plan to make a $$40,000$ contribution to your individual retirement account, at $3\mathrm{.}5$ percent per year on average. Compute how much it will be worth if you deposit it for $25$ years.

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Q$3.$ Repeat Q$1-$Q$2,$ when the interest rate is being componded every SIX MONTHS $($or SEMIANNUALLY$].$

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Q$4.$ Erica is purchasing a financial instrument that will pay $$5,000$ a year for seven years, at the end of every year.

How much should she pay for this investment today if she wishes to earn a $12$ percent rate of return?

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Q$5.$ Repeat Q$5,$ when you are committed to making contributions at the beginning of every year.

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Q$6.$ Solve for $x$ : Jane recently purchased a new home with a mortgage of $$x.$ She financed it at $6\mathrm{.}6$ percent interest with annual installments of $$36,000$ for thirty years.

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Q$7.$ Solve for $x$ : Jane recently purchased a new home with a mortgage of $$x.$ She financed it at $6\mathrm{.}6$ percent interest with MONTHLY installments of $3,000$ for $360$ months.