Find the present value of an annuity due that pays $\$ 3000$ at the beginning of each quarter for the next $7$ years. Assume that money is worth $5.8 \%$ compounded quarterly.

A contractor builds a swimming pool with cross section in the shape of a trapezoid. The deep end is 8ft deep and the shallow end is 3ft deep. The length of the pool is 50ft and the width is 20ft. As the pool is being filled, find the volume of water when the depth is 4ft.

Suppose that a $10$-year corporate bond has a maturity value of $\$ 10,000$ and a coupon rate of $10 \%$, with coupons paid semiannually. Find the market price of the bond if the current yield rate is $6 \%$ compounded semiannually. Is this bond selling at a discount or at premium?

Is there any difference between the present values in parts (a) and (b)? Explain.

(a) An annuity due that pays $\$ 1000$ at the beginning of each year for $10$ years

(b) Taking $\$ 1000$ now and establishing an ordinary annuity that pays $\$ 1000$ at the end of each year for $9$ years

A student has a savings account earning $9 \%$ simple interest. She must pay $\$ 1500$ for first-semester tuition by September $1$ and $\$ 1500$ for second-semester tuition by January $1$. How much must she earn in the summer (by September $1$) to pay the first-semester bill on time and still have the remainder of her summer earnings grow to $\$ 1500$ between September $1$ and January $1$?

A couple borrows $\$ 180,000$ at $5.4 \%$ compounded monthly for $30$ years. After making $80$ payments of $\$ 1010.76$, they refinance at $4.8 \%$ compounded monthly for $25$ years, with refinancing costs of $\$ 550$ added to the new loan.

(a) Find the amount refinanced.

(b) Find the new monthly payment.

( c ) How much is saved by refinancing?

Which of the following is included in the calculation of the quick (acid-test) ratio? a. Prepaid expenses and cash b. Cash and accounts receivable c. Inventory and short-term investments d. Inventory and prepaid expenses

Find the future value of an annuity due of $\$ 1500$ each month for $3$ years if the interest rate is $12 \%$ compounded monthly.

Describe a debt to be amortized. In each problem, find: (a) the size of each payment,

(b) the total amount paid for each purchase,

( c ) the total interest paid over the life of the loan.

A man buys a house for $\$ 350,000$. He makes a $\$ 150,000$ down payment and amortizes the rest of the purchase price with semiannual payments over the next $10$ years. The interest rate on the debt is $12 \%$ compounded semiannually.

Find the interest that will result if $\$ 8000$ is invested at $7 \%$ compounded continuously for $8$ years.

Interest If $\$ 1000$ is invested for $4$ years at $8 \%$ compounded quarterly, how much interest will be earned?

Explain the difference between an ordinary annuity and an annuity due.

Calculate lower and upper bounds for the following calculations, if each of the numbers is given to the nearest whole number. a) $14 \times 20$ b) $135 \times 25$ c) $100 \times 50$ d) $\frac{40}{10}$ e) $\frac{33}{11}$ f) $\frac{125}{15}$ g) $\frac{12 \times 65}{16}$ h) $\frac{101 \times 28}{69}$ i) $\frac{250 \times 7}{100}$ j) $\frac{44}{3^{2}}$ k) $\frac{578}{17 \times 22}$ l) $\frac{1000}{4 \times(3+8)}$

A firm buys $12$ file cabinets at $\$ 140$ each, with payment in full due in $90$ days. How much must the firm deposit now to have enough to pay the bill if money is worth $3 \%$ simple interest per year? Use $360$ days in a year.