Eight scenarios are described below. Each scenario describes a series of payments. Determine whether or not the series of payments is an annuity, and if it is$,$ whether the annuity is ordinary or due. Also determine whether the amount asked for is the present or future value.

Match each scenario to to choice which describes it$.$ Note that choices can be used more than once, and that all the choices may or may not be used.

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Thirty years ago, Blaise started putting $$2,500$ into his IRA at the start of each year. His account has earned $11\mathrm{.}3\%.$ How much does he have in this account today?

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Five years ago, Dave and Jess started setting aside $$500$ in savings towards a down payment on a house at the start of each month. They deposited the money in an account that has paid $3\mathrm{.}75\%.$ How much do they have saved up today?

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Assuming an interest rate of $6\%,$ how much would it be worth to Cattarauqua Ginseng Enterprises to invest in a new inventory management system which would save them $$42,500$ per year for eight years?

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Because of injuries I experienced using one of their products, Dangertoys Inc is required to pay me $$40,000$ per year at the start of each year for the next $20$ years. An investment banker has offered to give me a lump sum today for these payments, calculated using a $9\%$ interest rate.

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Dylar Pharmaceuticals is being sued by several states over their marketing of a drug which proved to be harmful and ineffective. They became aware of the problem and started setting money aside to prepare for this liability five years ago. Each year they have set aside $$7,500,000$ into a fund earning $4\mathrm{.}5\%.$ How much do they having in this fund now?

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Faber College has been able to raise $$700,000$ per year from an alumni fundraising appeal in each of the last $12$ years. This $$700,000$ per year has been invested at $8\%.$ How much has this money grown to today?

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I just took out a loan to buy a new car. The payments will be $$379\mathrm{.}53$ per month for the next $60$ months. How much did I borrow?

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Falstaff College is undertaking a ten$-$year program to raise money to endow a new scholarship program. The goal is to raise enough money to be able to fund $$1,000,000$ in scholarships annually for the next thirty years. The funds will be invested and are expected to earn a $5\%$ growth rate. How much does the college need to raise to establish this fund?

$1.$

Future value, ordinary annuity

$2.$

Future value, annuity due

$3.$

Present value, ordinary annuity

$4.$

Present value, annuity due

$5.$

Not an annuity