Total Inc. recently purchased a new office building costing $15 million. The firm financed this purchase at 6 percent APR with quarterly compounding. Quarterly payments starting from next quarter will be $400,000. How many years will it take the firm to pay off this debt

13.88 years

Explanation:

Using the formula for present value  for an annuity with constant payment of $ 400000

PV = P ( 1 - ( 1+r)^-n) / r

where P = $ 400000, r = 6%/4 = 1.5 % = 0.015 and PV =  $15 million

 $15 million = $400000(1 - ( 1 + 0.015) ^-n / 0.015

$ 15 000000 × 0.015 / $ 400000 =(1 - ( 1 + 0.015) ^-n)

 ( 1 + 0.015) ^-n = 1 - 0.5625

1.015^-n = 0.4375

take log of  both side

-n log 1.015 = log 0.4375

-n = log 0.4375 / log 1.015 = -55.52

n = 55.52

in years = 55.52 / 4 =13.88 years

13.88 years

Explanation:

Since the quarterly payments starting from next quarter, the relevant formula to use is the present value (PV) of an ordinary annuity formula stated as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)

Where;

PV = Present value or the office building cost today = $15,000,000

P = quarterly payment = $400,000

r = APR = 6%, 0.06 annually = 0.06/4 quarterly = 0.015

n = number of quarters = ?

Substitute the values into equation (1) to have:

15,000,000 = 400,000 × {1 - [1 ÷ (1 + 0.015)]^n} ÷ 0.015

15,000,000 × 0.015 = 400,000 × {1 - [1 ÷ (1.015)]^n}

225,000 ÷ 400,000 = 1 - [1 ÷ 1.015]^n

0.5625 = 1 - (0.985221674876847)^n

0.5625 - 1 = - (0.985221674876847)^n

- 0.4375 = - (0.985221674876847)^n

Both sides by minus one, we have:

(0.985221674876847)^n = 0.4375

Loglinearising both sides, we have:

n × ln(0.985221674876847) = ln(0.4375)

n = ln(0.4375) ÷ ln(0.985221674876847)

n =  (- 0.826678573184468) ÷ (- 0.0148886124937505)

n = 55.52  quarters

We can now convert it to years by as follows:

n = 55.52  quarters ÷ 4 = 13.88 years

personnel management.

Explanation:

Training new personnel who just started working at the office fits under personnel management.

Personnel management can be defined as an administrative task or function which primarily involves the process of hiring employees and developing or training them to become beneficial and valuable for the growth and development of the company.

Hence, the main purpose and focus of personnel management is to provide a quality workforce necessary to successfully achieve the organizational set goals and objectives.