Interest on investments, 3 factors affect their growth - Correct Answers 1. Interest rate
2. The type of interest
3. The time period during which the invested principal earns interest
Interest rates - Correct Answers Remember that interest is a fee that individuals and financial
institutions pay (or charge) for the use of borrowed money. And the amount of interest earnings
depends on the interest rate that's applied to the principal.
Interest rates are usually stated in decimal form, so a 5 percent interest rate appears as 0.05 and a 2.5
percent rate appears as 0.025.
Interest earned = $1,000 × 0.025 = $25
Calculating Interest Earned - Correct Answers Principal (regular amount) × Interest rate = Interest
earned
Interest rate - Correct Answers Interest rate = Interest amount ÷ Principal
simple interest - Correct Answers the amount of interest earned for one year is equal to the principal
multiplied by the interest rate. As a result, when an investment earns simple interest, the nominal
interest rate and the effective interest rate are the same.
The total amount of simple interest earned is equal to the interest for one year multiplied by the
number of years in the investment period.
At a constant annual rate of 5% simple interest, after 100 years the $10 account would have earned $50
in interest (100 x $0.50), and the total value of the investment would be $60.00.
Compound interest - Correct Answers When interest is compounded, the interest earned each
investment period is added to the original principal amount, and that total is used as the beginning
,balance when calculating interest earnings for the next period. In this case, the effective interest rate is
greater than the nominal interest rate.
Compound Interest:
At a constant annual rate of 5% compound interest, after 100 years the $10 investment would have
earned $1,305.01 in interest and the total value of the investment would be $1,315.01.
Effective Interest Rate - Correct Answers The type of interest rate that includes the effects of
compounding.
The Rule of 72 - Correct Answers Investors can use a simple rule of thumb known as the Rule of 72 to
estimate how fast a principal sum doubles at a specified compound interest rate. The Rule of 72 states
that, for a known interest rate, under annual compounding, the approximate number of years for a
principal sum to double is 72 divided by the interest rate.
Years to double = 72 ÷ Interest rate
Steadfast Insurance can calculate the interest amount it earned on an initial sum of money invested for
one year at a specified interest rate by ( multiplying / dividing ) the principal by the interest rate.
multiplying
dividing - Correct Answers Multiplying- An investor can calculate the interest amount earned on an
initial sum of money invested for one year at a specified interest rate by multiplying the principal by the
interest rate.
Because ( simple / compound ) interest is applied to the same amount of principal each year, the
amount of interest earned each year is the same, found by multiplying the principal amount by the
interest rate.
simple
compound - Correct Answers simple- Because simple interest is applied to the same amount of principal
each year, the amount of interest earned each year is the same, found by multiplying the principal
amount by the interest rate.
Because the nominal interest rate includes the effects of compounding, it's usually greater than the
effective interest rate.
,True
False - Correct Answers False- Because the effective interest rate includes the effects of compounding,
it's usually greater than the nominal interest rate. And it increases even more if interest is compounded
more than once each year.
Steadfast Insurance can use the Rule of 72 to
A. Estimate how fast a principal sum doubles at a specified compound interest rate
B. Determine the rate of interest a principal sum must earn to double in a certain number of years.
Both A and B
A only
B only
Neither A nor B - Correct Answers The Rule of 72 states that, for a known interest rate, under annual
compounding, the approximate number of years for a principal sum to double is 72 divided by the
interest rate.The Rule of 72 can also help determine the rate of interest a principal sum must earn to
double in a certain number of years.
So far, you've seen how factors such as interest rates, types of interest, and time affect investment
values. How do you think insurers use this information? (Choose all that apply.) - Correct Answers The
time value of money (TVOM) concept explains the effects of interest rates, types of interest, and time
on investment values. Insurers use TVOM to determine the future value of an investment and the
amount they need to invest today to earn a given amount in the future. TVOM doesn't help with
investment choices.
TVOM - Correct Answers Insurers rely on the concept of the time value of money (TVOM) to explain the
relationships among payment amounts, interest rates, and time.According to this concept, a sum of
money has both a present value (PV) and a future value (FV).
Present value - Correct Answers In simple terms, the present value of an investment is the principal
the original amount invested before it's affected by interest.
Present value = Principal
Future value - Correct Answers The future value is the invested principal plus the interest generated by
the investment over time.
Future value = Principal + Interest earned
, The following statement(s) can correctly be made about present value and future value:
A. Generally, a sum of money invested today has a present value that is less than its future value
because of interest.
B. A sum of money invested today for 10 years will grow to a larger sum than the same amount of
money invested for 5 years.
Both A and B
A only
B only
Neither A nor B - Correct Answers In the next part of the lesson, we'll take a closer look at future values.
FV for single amount - Correct Answers Analysts typically substitute present value (PV) for principal
because, like principal, present value represents a sum of money before it is affected by interest. So, the
formula for calculating the future value (FV) of a single amount for one period is
FV = PV + Interest earned
FV for one year investment - Correct Answers For a one-year period, the amount of interest earned
equals the present value multiplied by the interest rate, i. Because compounding only occurs when
money is held for more than one period, we don't specify a value for the number of interest periods, n.
We can express the formula for the interest earned on a one-year investment as follows:
Interest earned = PV × i
Elegant Financial invested $300,000 for one year at 5 percent interest. How much did Elegant have at
the end of the year?
___________ = PV × (1 + i )
$1,500,000
$450,000
$315,000 - Correct Answers 315,000
Fv of a single amount for mutiple periods - Correct Answers The general formula for finding the future
value of an investment earning compound interest, i, for n periods, can be written as:
FV = PV × (1 + i )n
2. The type of interest
3. The time period during which the invested principal earns interest
Interest rates - Correct Answers Remember that interest is a fee that individuals and financial
institutions pay (or charge) for the use of borrowed money. And the amount of interest earnings
depends on the interest rate that's applied to the principal.
Interest rates are usually stated in decimal form, so a 5 percent interest rate appears as 0.05 and a 2.5
percent rate appears as 0.025.
Interest earned = $1,000 × 0.025 = $25
Calculating Interest Earned - Correct Answers Principal (regular amount) × Interest rate = Interest
earned
Interest rate - Correct Answers Interest rate = Interest amount ÷ Principal
simple interest - Correct Answers the amount of interest earned for one year is equal to the principal
multiplied by the interest rate. As a result, when an investment earns simple interest, the nominal
interest rate and the effective interest rate are the same.
The total amount of simple interest earned is equal to the interest for one year multiplied by the
number of years in the investment period.
At a constant annual rate of 5% simple interest, after 100 years the $10 account would have earned $50
in interest (100 x $0.50), and the total value of the investment would be $60.00.
Compound interest - Correct Answers When interest is compounded, the interest earned each
investment period is added to the original principal amount, and that total is used as the beginning
,balance when calculating interest earnings for the next period. In this case, the effective interest rate is
greater than the nominal interest rate.
Compound Interest:
At a constant annual rate of 5% compound interest, after 100 years the $10 investment would have
earned $1,305.01 in interest and the total value of the investment would be $1,315.01.
Effective Interest Rate - Correct Answers The type of interest rate that includes the effects of
compounding.
The Rule of 72 - Correct Answers Investors can use a simple rule of thumb known as the Rule of 72 to
estimate how fast a principal sum doubles at a specified compound interest rate. The Rule of 72 states
that, for a known interest rate, under annual compounding, the approximate number of years for a
principal sum to double is 72 divided by the interest rate.
Years to double = 72 ÷ Interest rate
Steadfast Insurance can calculate the interest amount it earned on an initial sum of money invested for
one year at a specified interest rate by ( multiplying / dividing ) the principal by the interest rate.
multiplying
dividing - Correct Answers Multiplying- An investor can calculate the interest amount earned on an
initial sum of money invested for one year at a specified interest rate by multiplying the principal by the
interest rate.
Because ( simple / compound ) interest is applied to the same amount of principal each year, the
amount of interest earned each year is the same, found by multiplying the principal amount by the
interest rate.
simple
compound - Correct Answers simple- Because simple interest is applied to the same amount of principal
each year, the amount of interest earned each year is the same, found by multiplying the principal
amount by the interest rate.
Because the nominal interest rate includes the effects of compounding, it's usually greater than the
effective interest rate.
,True
False - Correct Answers False- Because the effective interest rate includes the effects of compounding,
it's usually greater than the nominal interest rate. And it increases even more if interest is compounded
more than once each year.
Steadfast Insurance can use the Rule of 72 to
A. Estimate how fast a principal sum doubles at a specified compound interest rate
B. Determine the rate of interest a principal sum must earn to double in a certain number of years.
Both A and B
A only
B only
Neither A nor B - Correct Answers The Rule of 72 states that, for a known interest rate, under annual
compounding, the approximate number of years for a principal sum to double is 72 divided by the
interest rate.The Rule of 72 can also help determine the rate of interest a principal sum must earn to
double in a certain number of years.
So far, you've seen how factors such as interest rates, types of interest, and time affect investment
values. How do you think insurers use this information? (Choose all that apply.) - Correct Answers The
time value of money (TVOM) concept explains the effects of interest rates, types of interest, and time
on investment values. Insurers use TVOM to determine the future value of an investment and the
amount they need to invest today to earn a given amount in the future. TVOM doesn't help with
investment choices.
TVOM - Correct Answers Insurers rely on the concept of the time value of money (TVOM) to explain the
relationships among payment amounts, interest rates, and time.According to this concept, a sum of
money has both a present value (PV) and a future value (FV).
Present value - Correct Answers In simple terms, the present value of an investment is the principal
the original amount invested before it's affected by interest.
Present value = Principal
Future value - Correct Answers The future value is the invested principal plus the interest generated by
the investment over time.
Future value = Principal + Interest earned
, The following statement(s) can correctly be made about present value and future value:
A. Generally, a sum of money invested today has a present value that is less than its future value
because of interest.
B. A sum of money invested today for 10 years will grow to a larger sum than the same amount of
money invested for 5 years.
Both A and B
A only
B only
Neither A nor B - Correct Answers In the next part of the lesson, we'll take a closer look at future values.
FV for single amount - Correct Answers Analysts typically substitute present value (PV) for principal
because, like principal, present value represents a sum of money before it is affected by interest. So, the
formula for calculating the future value (FV) of a single amount for one period is
FV = PV + Interest earned
FV for one year investment - Correct Answers For a one-year period, the amount of interest earned
equals the present value multiplied by the interest rate, i. Because compounding only occurs when
money is held for more than one period, we don't specify a value for the number of interest periods, n.
We can express the formula for the interest earned on a one-year investment as follows:
Interest earned = PV × i
Elegant Financial invested $300,000 for one year at 5 percent interest. How much did Elegant have at
the end of the year?
___________ = PV × (1 + i )
$1,500,000
$450,000
$315,000 - Correct Answers 315,000
Fv of a single amount for mutiple periods - Correct Answers The general formula for finding the future
value of an investment earning compound interest, i, for n periods, can be written as:
FV = PV × (1 + i )n
