(a) decide whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

Dr. Jane Kodiak plans to sell her practice to an HMO. The HMO will pay her $\$ 1.5$ million now or will make a $\$ 500,000$ partial payment now and additional payments of $\$ 140,000$ at the end of each year for the next $10$ years. If money is worth $6.5 \%$ compounded annually, is it better to take $\$ 1.5$ million now or $\$ 500,000$ now and $\$ 140,000$ at the end of each year for the next $10$ years? Justify your choice.

(a) state whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

If $\$ 1000$ is deposited at the beginning of each quarter into an account that earns $8 \%$ compounded quarterly, how long until the account contains $\$ 31,000$?

When Otto and Millie bought their home, they borrowed $\$ 200,000$ for $30$ years at $6 \%$ compounded monthly. After making $120$ payments of $\$ 1199.10$, they plan to refinance at $4.5 \%$ compounded monthly for $15$ years, with refinancing costs of $\$ 750$ added to the amount of the new loan.

(a) Find the amount of the new loan (amount refinanced).

(b) Find their new monthly payment.

( c ) Find the amount saved by refinancing.

Write the first seven terms of the sequence defined by $a_n=2 / n$.

Sinking fund How much would have to be invested at the end of each year at $6 \%$ compounded annually to pay off a debt of $\$ 80,000$ in $10$ years?

(a) decide whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

Is it more economical to buy an automobile for $\$ 29,000$ cash or to pay $\$ 8000$ down and $\$ 3000$ at the end of each quarter for $2$ years, if money is worth $8 \%$ compounded quarterly?

(a) decide whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

A company wants to have $\$ 40,000$ at the beginning of each $6$-month period for the next $4 \frac{1}{2}$ years. If an annuity is set up for this purpose, how much must be invested now if the annuity earns $6.68 \%$ compounded semiannually?

Write the first ten terms of the sequence defined by $a_n=3 n$.

(a) state whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

How much must be invested at the beginning of each year at $10 \%$ compounded annually to pay off a debt of $\$ 50,000$ in $8$ years?

Annuity Find the future value of an ordinary annuity of $\$ 800$ paid at the end of every $6$-month period for $10$ years, if it earns interest at $12 \%$ compounded semiannually.

Rank each interest rate and compounding scheme in order from highest yield to lowest yield.

$8 \%$ compounded quarterly, $8 \%$ compounded monthly, $8 \%$ compounded annually

A company that purchases a piece of equipment by borrowing $\$ 250,000$ for $10$ years at $6 \%$ compounded monthly has monthly payments of $\$ 2775.51$.

(a) Find the unpaid balance on this loan after $1$ year.

(b) During that first year, how much interest does the company pay?

Suppose you lent $\$ 5000$ to friend $1$ for $18$ months at an annual simple interest rate of $9 \%$. After $1$ year, you need money for an emergency and decide to sell the note to friend $2$.

(a) How much does friend $1$ owe when the loan is due?

(b) If your agreement with friend $2$ means that she earns simple interest at an annual rate of $12 \%$, how much did friend $2$ pay you for the note?

What is the annual percentage yield (or effective annual rate) for a nominal rate of (a) $8.4 \%$ compounded quarterly and (b) $10\%$ compounded continuously?