**This section of sample problems and solutions is a part of** **The Actuary’s Free Study Guide for Exam 5, authored by Mr. Stolyarov. This is Section 3 of the Study Guide. See an index of all sections by following the link in this paragraph.**

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of *Basic Ratemaking*, cited below. Students are encouraged to read these pages before attempting the problems.

**Source: **

*Loss Models: From Data to Decisions,*(Third Edition), 2008, by Klugman, S.A., Panjer, H.H. and Willmot, G.E., Chapter 1, pp. 4-5.

**Original Problems and Solutions from The Actuary’s Free Study Guide**

**Problem S5-3-1.** Which of the following are components of *underwriting expenses*? More than one answer may be correct.

(a) Taxes, licenses, and fees

(b) General expenses

(c) Insured losses

(d) Loss adjustment expenses

(e) Claims-related expenses

(f) Other acquisition expenses

(g) Commissions and brokerage

(h) Charitable donations of the insurance company

**Solution S5-3-1.** The following are the correct answers, as identified in Werner and Modlin (4): **(a)** Taxes, licenses, and fees **(b)** General expenses

**(f)** Other acquisition expenses **(g)** Commissions and brokerage

**Problem S5-3-2.** What are the two components of insurance company profit?

(a) Underwriting profit and legal settlements

(b) Investment income and earned premium

(c) Underwriting profit and loss adjustment profit

(d) Earned premium and unearned premium

(e) Underwriting profit and investment income

(f) The money the company earned and the money the company did not earn

**Solution S5-3-2.** The correct answer, as identified in Werner and Modlin (5), is

**(e)** Underwriting profit and investment income.

**Problem S5-3-3.** An insurance company’s underwriting profit is 3500, and its underwriting expenses are 2000. Losses are 90000, and loss adjustment expenses are 3560. Use the fundamental insurance equation to determine the amount of premium.

**Solution S5-3-3.** The fundamental insurance equation is

Premium= Losses + LAE + UW Expenses + UW Profit.

We are given Losses = 90000, LAE = 3560, UW Profit = 3500, UW Expenses = 2000, so

Premium = 90000 + 3560 + 3500 + 2000 = **Premium = 99060**.

**Problem S5-3-4.** The amount of premium is 6490, underwriting profit is 360, underwriting expense are 1000, and loss adjustment expenses are 460. Use the fundamental insurance equation to determine the amount of losses.

**Solution S5-3-4.** The fundamental insurance equation is

Premium= Losses + LAE + UW Expenses + UW Profit.

Thus, Losses = Premium – LAE – UW Expenses – UW Profit =

6490 – 460 – 1000 – 360 = **Losses = 4670**.

**Problem S5-3-5.** The amount of premium is 5460, losses are 3660, underwriting expenses are 1234, underwriting profit is 100, and allocated loss adjustment expenses are 345. Find the unallocated loss adjustment expenses using the fundamental insurance equation.

**Solution S5-3-5.** The fundamental insurance equation is

Premium= Losses + LAE + UW Expenses + UW Profit.

We also know that LAE = ALAE + ULAE.

Thus, Premium = Losses + ALAE + ULAE + UW Expenses + UW Profit, meaning that

ULAE = Premium – Losses – ALAE – UW Expenses – UW Profit =

5460 – 3660 – 345 – 1234 – 100 = **ULAE = 121**.

**See other sections of The Actuary’s Free Study Guide for Exam 5.**