Lesson 8

Question 1

8.1.1 Explain the difference between simple interest and compound

Answer 1

Simple is only accrued on the principal. Compound accrues interest on interest.

Question 2

8.1.2 Misha wants to buy a new automobile that is currently priced at $45,000. She
presently has $40,000 and can earn 8% per year compounded annually for the next
two years. Evaluate whether she will be able to purchase the car at the end of two
years if the price of the car increases by 2% per year. (

Answer 2

Misha will be $162 short

Question 3

8.1.3 Assume two investments of $100 each are made at an interest rate of 6% per
year compounded annually. Calculate their value at the end of two years if one
investment earns simple interest and the other earns compound interest. Determine
the difference in the amount of interest earned under the two investments

Answer 3

112.36 compound

112 simple

Question 4

8.1.4 Explain the difference between a nominal interest rate and an effective annual rate

Answer 4

A nominal interest rate is the contracted or quoted interest rate - simple

An effective annual rate is the annual rate of interest being earned each year including the impact of compounding

Question 5

8.1.5 Determine the effective annual rate equivalent to a nominal rate of 12% per annum
compounded every two months.

Answer 5

12.616%

EAR = (1 + (12% / 6))^6 - 1

Question 6

8.1.6 Describe the impact on the future value of a sum of money if either the interest rates or the time horizon increases

Answer 6

The longer the time horizon the higher the future value

The higher the interest rates the higher the future value

Question 7

8.1.7 Riverview Hotel Group paid the following monthly insurance premiums in the first
half of 2017:

January 1, 2017 - $400
February 1, 2017 - $450
March 1, 2017 - $500
April 1, 2017 - $550
May 1, 2017 - $600
June 1, 2017 - $650

Assuming an interest rate of 2% per month compounded monthly, calculate the
future value of the total premium paid at July 1, 2017

Answer 7

$3,359.43

Question 8

8.1.8 Rotunda Engineering is expecting to hire a number of new employees over the next
36 months due to several large development contracts that were signed recently.
If the company currently employs 150 people and is projecting average growth of
1% per month, calculate the total number of employees at the end of the three-year
period.

Answer 8

215

Question 9

8.2.1 Explain discounting and discount rate

Answer 9

Discounting refers to finding the PV of one or more cashflows

A discount rate is the rate used to calculate the PV of future cash flows. It is also referred to as the interest rate

Question 10

8.2.2 Riverview Hotel Group paid the following monthly insurance premiums in the first
half of 2017:

January 1, 2017 $400
February 1, 2017 $450
March 1, 2017 $500
April 1, 2017 $550
May 1, 2017 $600
June 1, 2017 $650

Calculate the present value of the Riverview Hotel Group premiums valued at January 1, 2017. 2% compounded monthly

Answer 10

$2,983.08

Question 11

8.2.3 Explain what happens to the present value of a sum of money if either the interest rates or the time horizon increases

Answer 11

The longer the time horizon the lower the present value

The higher the discount rate the lower the present value

Question 12

8.2.3 An insurer is holding a certain amount of reserves for all future annuity payments
to its living policyholders. If, on average, these policyholders live 0.8 years longer,
describe the implications for the insurer’s ability to meet future obligations.

Answer 12

Since policyholders are living longer the insurer would need to make additional payments.

This means that the amount of reserves originally set aside meet the future obligations would be insufficient

Question 13

8.2.5 An insurer is holding a certain amount of reserves for all future benefit payments.
The current reserve level was determined based on an annual interest rate of 5%. If
the insurer can only earn 4% per year in practice, evaluate what would happen to
the insurer’s ability to meet future obligations

Answer 13

This would mean the insurer would not be sufficient and would need to be increased

Question 14

8.2.6 Bridgetown Insurance Company is expecting to pay total death benefits of
$2,000,000 at the end of 20 years. Assuming that the interest rate is 7% per year
compounded annually, calculate the reserve level that must be held today to
meet this future obligation. Calculate using both the formula method and the table
method.

Answer 14

516,838 calculated

from the PV table 516,840. the difference is due to rounding in the table

Question 15

8.3.1 True Test Insurance Company has established a reserve of $10,000 and will have to
pay out a life insurance benefit of $100,000 in 30 years. Calculate the annual rate of
interest that must be earned in order to meet this obligation.

Answer 15

7.98%

Question 16

8.3.2 A one-year investment will provide a payback of $1,350 for an initial cash outlay of
$1,250. Calculate the annual interest rate earned on this investment.

Answer 16

8%

Question 17

8.3.3 Far East Insurance Company has established a waiver of premium reserve of
$100,000 and will have to pay out an optional life insurance benefit of $200,000. With
an interest rate of 6% compounded annually, calculate how many years it will take
for the reserve of $100,000 to accumulate to $200,000

Answer 17

11.9 years

Question 18

8.3.4 Calculate the approximate nominal rate of interest, compounded semiannually,
that has been earned on $2,000 if the future value at the end of five years is $2,700.

Answer 18

The nominal rate of interest earned is just over 6%

The interest rate can be determined by using the future value table (refer to Study
Guide Module 8, page 55) to find the rate that coincides with n 5 10 periods and (1
1 r)10 5 1.35. The closest interest rate in the table is equal to 3%, which is a nominal
6% interest rate, compounded semiannually.

Question 19

8.4.1 Far Point Assurance Company receives premiums of $150,000 at the end of each
month from its largest client. Calculate the future value of 12 monthly premium
payments if the interest rate is 9.2% compounded semiannually.

Answer 19

FVA = $1,876,137.95 calculated

FVA = $1,876,138.50 if you use the table in the book

Question 20

8.4.2 The beneficiary of a life insurance policy is to receive $1,000 at the end of each
year for five years. Determine the present value of these payments assuming an
interest rate of 6% per year compounded annually. (

Answer 20

PVA = $4,212.36 calculated

PVA = $4,212.36 using the table at the end of the book

Question 21

8.4.3 Based on the information provided in question 4.2, determine the future value of
the beneficiary’s payments at the end of five years.

Answer 21

PVA = $5,637.09 calculated

PVA = $5,637.09 using the table at the end of the book

Question 22

8.4.4 State the differences between an ordinary annuity and an annuity due.

Answer 22

An annuity due has the cashflow due at the beginning of the period

Question 23

8.4.5 Determine by what ratio the future value of an annuity due of $500 for five years at a
5% effective annual rate will exceed the future value of an ordinary annuity of the
same amount, time horizon and rate of interest

Answer 23

The FV of an annuity due will exceed the FV of an ordinary annuity since the annuity due will be paid at the beginning of the period and the ordinary annuity is paid at the end of the period

Question 24

8.4.6 Identify steps involved in calculating the value of an annuity due.

Answer 24

1) Calculate the PV as though it were an ordinary annuity

2) Multiplying the answer by (1+r)

Question 25

8.4.7 Mr. Bethune is currently receiving a long-term disability (LTD) benefit of $2,400,
payable at the end of each month. If there are 90 benefit payments remaining and he
can earn an interest rate of 0.5% compounded monthly, calculate the future value
of the series of remaining LTD payments

Answer 25

FVA = $271,946.25