Construction fund A company wants to have $\$ 250,000$ available in $4 \frac{1}{2}$ years for new construction. How much must be deposited at the beginning of each quarter to reach this goal if the investment earns $10.2 \%$ compounded quarterly?

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

A family wants to have a $\$ 200,000$ college fund for their children at the end of $20$ years. What contribution must be made at the end of each quarter if their investment pays $7.6 \%$ compounded quarterly?

To upgrade its equipment, Simon Reilly Chemicals (SRC) borrowed $\$ 2.8$ million at $6.4 \%$ compounded quarterly for $20$ years. After making $18$ quarterly payments of $\$ 62,297.39$, SRC plans to refinance this loan at $5.2 \%$ compounded quarterly for $10$ years, with refinancing charges of $\$ 12,000$ added to the amount refinanced.

(a) Find the amount refinanced.

(b) Find SRC's new quarterly payment.

( c ) Find the amount saved by refinancing.

(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.

What would you pay for a $100,000 debenture bond that matures in 15 years and pays$5,000 a year in interest if you wanted to earn a yield of:

• a. 4%?
• b. 5%?
• c. 6%?

Write the first six terms of the sequence whose $n$th term is $(-1)^n /(2 n+1)$.

Write the first six terms of the sequence whose $n$th term is $(-1)^n /(2 n+1)$.

The following account balances were included in the trial balance of Twain Corporation at June 30, 2020.

$$\begin{array}{lrrllrrr} \text{Sales revenue}&&\$1,578,500&\hspace{10pt}&\text{Depreciation expense (office furniture and equipment)}&&\$7,250\\ \text{Sales discounts}&&31,150&\hspace{10pt}&\text{Property tax expense}&&7,320\\ \text{Cost of goods sold}&&896,770&\hspace{10pt}&\text{Bad debt expense (selling)}&&4,850\\ \text{Salaries and wages expense (sales)}&&56,260&\hspace{10pt}&\text{Maintenance and repairs expense (administration)}&&9,130\\ \text{Sales commissions}&&97,600&\hspace{10pt}&\text{Office expense}&&6,000\\ \text{Travel expense (salespersons)}&&28,930&\hspace{10pt}&\text{Sales returns and allowances}&&62,300\\ \text{Delivery expense}&&21,400&\hspace{10pt}&\text{Dividends received}&&38,000\\ \text{Entertainment expense}&&14,820&\hspace{10pt}&\text{Interest expense}&&18,000\\ \text{Telephone and Internet expense (sales)}&&9,030&\hspace{10pt}&\text{Income tax expense}&&102,000\\ \text{Depreciation expense (sales equipment)}&&4,980&\hspace{10pt}&\text{Depreciation understatement due to error-2017 (net of tax)}&&17,700\\ \text{Maintenance and repairs expense (sales)}&&6,200&\hspace{10pt}&\text{Dividends declared on preferred stock}&&9,000\\ \text{Miscellaneous selling expenses}&&4,715&\hspace{10pt}&\text{Dividends declared on common stock}&&37,000\\ \text{Office supplies used}&&3,450&\hspace{10pt}&\text{}&&\\ \text{Telephone and Internet expense (administration)}&&2,820&\hspace{10pt}&\text{}&&\\ \text{}&&&\hspace{10pt}&\text{}&&\\ \end{array}$$

The Retained Earnings account had a balance of $337,000 at July 1, 2019. There are 80,000 shares of common stock outstanding.

Instructions

a. Using the multiple-step form, prepare an income statement and a retained earnings statement for the year ended June 30, 2020.

b. Using the single-step form, prepare an income statement and a retained earnings statement for the year ended June 30, 2020.

Two different investment companies offer college savings plans, one at $8.2 \%$ compounded continuously and the other at $8.4 \%$ compounded quarterly. Which is the better investment?

(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?

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.

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

$6 \%$ compounded continuously, $6 \%$ compounded semiannually, $6 \%$ compounded monthly

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) 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 $\$ 31,000$?