LOMA 308 EXAMINATION 2025/2026 QUESTIONS WITH
SOLUTIONS GRADED A+
✔✔Montague Funds invested $100,000 at 3 percent interest compounded semi-
annually. Montague wants to know what its investment will be worth in two years. When
finding the future value of its investment, what value should Montague use for the
number of periods and the interest rate?
number of periods = 2, interest rate = 3
number of periods = 2, interest rate = 1.5
number of periods = 4, interest rate = 1.5
number of periods = 4, interest rate = 3 - ✔✔nUMBER OF PERIODS = 4, INTEREST
RATE = 1.5 - When interest is compounded more often than annually, you find the
number of compounding periods by multiplying the number of years a sum is invested
by the number of compounding periods in a year (2 years x 2 compounding periods per
year = 4 periods). You then adjust the interest rate by dividing the stated interest rate by
the number of compounding periods each year (3 ÷ 2 = 1.5).
✔✔One true statement about a future value interest factor (FVIF) table is that:
For any given period of time and any given interest rate, the FVIF is always greater than
1.
For any given period of time, FVIF values increase as the interest rate decreases.
For any given interest rate, FVIF values decrease as the investment period increases.
To find the future value of a sum greater than $1 at a given rate of interest for a stated
number of periods, we mutiply the FVIF value by the number of periods. - ✔✔For any
given period of time and any given interest rate, the FVIF is always greater than 1.
For any given period of time, FVIF values increase as the interest rate increases.For
any given interest rate, FVIF values increase as the investment period increases. To
find the future value of a sum greater than $1, multiply the FVIF value by the sum.
✔✔Durham Financial invested $100,000 at 4 percent interest compounded quarterly.
Using the FVIF Table above, what will be the value of Durham's investment in one
year?
$104,000
$104,060
101,000
That's correct! - ✔✔$104,060 To calculate the future value, multiply the number of years
by the number of compounding periods per year (1 × 4 = 4) to get the number of
periods. Then divide the interest rate by the number of compounding periods per year to
get the interest rate (4% ÷ 4 = 1). Then find the FVIF in our table for 4 periods at 1
percent interest (1.0406) and multiply that by the amount Durham invested ($100,000 x
1.0406) to give the correct answer of $104,060
,✔✔Annuities - ✔✔An annuity can refer to any series of payments that are equal in
amount and paid at regular intervals. An annuity does not refer to a series of unequal
payments or payments made at irregular intervals.
An annuity can refer to payments received or payments made.
An annuity is not the same as an annuity contract, which is a specific type of financial
product that can be structured to provide monthly income benefits. As a result, the
formulas used to calculate the values of an annuity are valid without any reference to an
actual annuity contract.
✔✔ordinary annuity - ✔✔payment made or received at the end of each annuity period.
A series of paychecks an employee receives at the end of each month
A series of interest payments on a bond
✔✔Annuity due - ✔✔payment made or received at the beginning of each annuity
period.
ex-
A series of rent payments made at the beginning of each month
A series of premiums for a life insurance policy paid at the beginning of each year
✔✔Future Value Interest Factors for an Annuity (FVIFAs) - ✔✔Analysts have developed
future value interest factors for annuities to simplify calculations, particularly for
annuities with large numbers of payments and compounding periods.These compound
interest factors, which are combined into tables, are called future value interest factors
for an annuity (FVIFAs). We can use FVIFAs to calculate the future value of an annuity
due or ordinary annuity the same way we used FVIFs to calculate the future value of a
sum of money.
✔✔Suppose that Jensen Financial invests $2,000,000 per year at an annual rate of 5
percent.
If Jenson makes each deposit on December 31, how much money will Jensen have in
20 years?
$66,132,000
$69,438,600
$64,132,000 - ✔✔Because Jensen makes payments at the end of each payment
period, its account is an ordinary annuity. To find the future value of an ordinary annuity,
we multiply the FVIFA factor for 20 periods at 5 percent interest by the amount of each
payment.FV of Jensen's ordinary annuity = $2,000,000 × 33.0660 = $66,132,000
✔✔Suppose that Jensen Financial invests $2,000,000 per year at an annual rate of 5
percent.If Jensen makes payments on the first day of the year instead of the last day,
how much money will Jensen have in 20 years?
$66,132,000
$69,438,600
,$71,438,600 - ✔✔Because Jensen makes its investment at the beginning of each
payment period, its account is an annuity due. To find the future value of an annuity
due, we multiply the amount of each payment by the FVIFA factor for (20 + 1) periods
and 5 percent interest and subtract the amount of one payment.FV of Jensen's annuity
due = $2,000,000 × 35.7193 = $71,438,600 - $2,000,000 = $69,438,600
✔✔Calculating the Present Value of a Single Amount for One Period - ✔✔- FV = PV ×
(1 + i )
- PV = FV ÷ (1 + i )
or
PV = FV × [1 ÷ (1 + i )]
✔✔calculating the present value of a single amount for multiple periods - ✔✔PV = FV ×
[1 ÷ (1 + i )2]
✔✔Which statement correctly describes the use of present value interest factors
(PVIFs)?
To find the present value of a sum, you must divide the future value by the PVIF.
For any given time period, as interest rates increase, PVIFs increase.
For any given time period and any given interest rate, PVIFs are always greater than 1.
For any given interest rate, as time increases, PVIF values decrease. - ✔✔To find the
present value, multiply the PVIF by a given future value. For any given time period, as
interest rates increase, PVIFs decrease. For any given time period and any given
interest rate, PVIFs are always less than 1.
✔✔Present Value of an Annuity Due and an Ordinary Annuity - ✔✔The present value of
an annuity, like the future value of an annuity, can be calculated for both an ordinary
annuity and an annuity due. Remember that the payment for an ordinary annuity is
made or received at the end of each annuity period, and that the payment for an annuity
due is made or received at the beginning of each annuity period.
The following time line represents the present value of an ordinary annuity of $100 per
year for three years. Note that, for an ordinary annuity, the valuation date for the present
value occurs at the beginning of the first period, which is one period before the first
payment is made.
✔✔Using PVIFAs: An Ordinary Annuity - ✔✔To calculate how much you need to invest
to provide payments of $1,000 at the end of each year for the next three years, you use
the PVIFA for 3 payments at 5 percent interest, which is 2.723. So the amount you will
need to invest today equals $1,000 × 2.723 = $2,723.00
✔✔Using PVIFAs: An Annuity Due - ✔✔To calculate how much you need to invest to
provide payments of $1,000 at the beginning of each year for the next three years, you
use the PVIFA for 2 payments at 5 percent interest, which is 1.859 and one payment of
$1,000. So the amount you will need to invest today equals ($1,000 × 1.859) + $1,000 =
$1,859 + $1,000 = $2,859.00
, ✔✔Important Insurer Applications of Present Values - ✔✔Insurers use PVIFs and
PVIFAs to determine the prices of one of their most important investments—bonds.
Remember that a bond pays periodic interest payments along with the payment of the
bond's par value upon maturity. So, to determine the price to pay for a bond, an insurer
must calculate two present values:
The present value of the bond's coupon payments, which represents the present value
of an ordinary annuity
The present value of the bond's par value, which is the present value of a single
payment
Future value of an ordinary annuity = periodic payment × FVIFA
Future value of an annuity due = periodic payment × FVIFA for one additional period -
one periodic payment
Present value of an ordinary annuity = periodic payment × PVIFA
Present value of an annuity due = periodic payment × PVIFA for one fewer period + one
periodic payment
✔✔Warwick Financial deposits $1,000,000 in an investment account on the first day of
each year. If Warwick contributes to the account for 6 years and the account earns 4
percent interest annually, what will be the value of the account?
What would we need to find to answer this question?
The future value of an ordinary annuity
The future value of an annuity due
The present value of an ordinary annuity
The present value of an annuity due - ✔✔future value of annuity due- We want to
determine the value of Warwick's money in the future, and because Warwick contributes
to the account at the beginning of the payment period, we need to find the future value
of an annuity due.
✔✔If Jonas Fund puts $1,000,000 in an investment each year on December 31, how
much will Jonas have at the end of 5 years? Assume the account earns 7 percent
interest.
What would we need to find to answer this question?
The future value of an ordinary annuity
The future value of an annuity due
The present value of an ordinary annuity
The present value of an annuity due - ✔✔Future value of an ordinary annuity- In this
situation, we are trying to find the future value of an ordinary annuity. We know this
because we need to determine the amount Jonas will have in the future, and Jonas
makes the investment on the last day of each year.
✔✔Future value of an ordinary annuity
Periodic payment × FVIFA
Periodic payment × FVIFA for one fewer period + one periodic payment
SOLUTIONS GRADED A+
✔✔Montague Funds invested $100,000 at 3 percent interest compounded semi-
annually. Montague wants to know what its investment will be worth in two years. When
finding the future value of its investment, what value should Montague use for the
number of periods and the interest rate?
number of periods = 2, interest rate = 3
number of periods = 2, interest rate = 1.5
number of periods = 4, interest rate = 1.5
number of periods = 4, interest rate = 3 - ✔✔nUMBER OF PERIODS = 4, INTEREST
RATE = 1.5 - When interest is compounded more often than annually, you find the
number of compounding periods by multiplying the number of years a sum is invested
by the number of compounding periods in a year (2 years x 2 compounding periods per
year = 4 periods). You then adjust the interest rate by dividing the stated interest rate by
the number of compounding periods each year (3 ÷ 2 = 1.5).
✔✔One true statement about a future value interest factor (FVIF) table is that:
For any given period of time and any given interest rate, the FVIF is always greater than
1.
For any given period of time, FVIF values increase as the interest rate decreases.
For any given interest rate, FVIF values decrease as the investment period increases.
To find the future value of a sum greater than $1 at a given rate of interest for a stated
number of periods, we mutiply the FVIF value by the number of periods. - ✔✔For any
given period of time and any given interest rate, the FVIF is always greater than 1.
For any given period of time, FVIF values increase as the interest rate increases.For
any given interest rate, FVIF values increase as the investment period increases. To
find the future value of a sum greater than $1, multiply the FVIF value by the sum.
✔✔Durham Financial invested $100,000 at 4 percent interest compounded quarterly.
Using the FVIF Table above, what will be the value of Durham's investment in one
year?
$104,000
$104,060
101,000
That's correct! - ✔✔$104,060 To calculate the future value, multiply the number of years
by the number of compounding periods per year (1 × 4 = 4) to get the number of
periods. Then divide the interest rate by the number of compounding periods per year to
get the interest rate (4% ÷ 4 = 1). Then find the FVIF in our table for 4 periods at 1
percent interest (1.0406) and multiply that by the amount Durham invested ($100,000 x
1.0406) to give the correct answer of $104,060
,✔✔Annuities - ✔✔An annuity can refer to any series of payments that are equal in
amount and paid at regular intervals. An annuity does not refer to a series of unequal
payments or payments made at irregular intervals.
An annuity can refer to payments received or payments made.
An annuity is not the same as an annuity contract, which is a specific type of financial
product that can be structured to provide monthly income benefits. As a result, the
formulas used to calculate the values of an annuity are valid without any reference to an
actual annuity contract.
✔✔ordinary annuity - ✔✔payment made or received at the end of each annuity period.
A series of paychecks an employee receives at the end of each month
A series of interest payments on a bond
✔✔Annuity due - ✔✔payment made or received at the beginning of each annuity
period.
ex-
A series of rent payments made at the beginning of each month
A series of premiums for a life insurance policy paid at the beginning of each year
✔✔Future Value Interest Factors for an Annuity (FVIFAs) - ✔✔Analysts have developed
future value interest factors for annuities to simplify calculations, particularly for
annuities with large numbers of payments and compounding periods.These compound
interest factors, which are combined into tables, are called future value interest factors
for an annuity (FVIFAs). We can use FVIFAs to calculate the future value of an annuity
due or ordinary annuity the same way we used FVIFs to calculate the future value of a
sum of money.
✔✔Suppose that Jensen Financial invests $2,000,000 per year at an annual rate of 5
percent.
If Jenson makes each deposit on December 31, how much money will Jensen have in
20 years?
$66,132,000
$69,438,600
$64,132,000 - ✔✔Because Jensen makes payments at the end of each payment
period, its account is an ordinary annuity. To find the future value of an ordinary annuity,
we multiply the FVIFA factor for 20 periods at 5 percent interest by the amount of each
payment.FV of Jensen's ordinary annuity = $2,000,000 × 33.0660 = $66,132,000
✔✔Suppose that Jensen Financial invests $2,000,000 per year at an annual rate of 5
percent.If Jensen makes payments on the first day of the year instead of the last day,
how much money will Jensen have in 20 years?
$66,132,000
$69,438,600
,$71,438,600 - ✔✔Because Jensen makes its investment at the beginning of each
payment period, its account is an annuity due. To find the future value of an annuity
due, we multiply the amount of each payment by the FVIFA factor for (20 + 1) periods
and 5 percent interest and subtract the amount of one payment.FV of Jensen's annuity
due = $2,000,000 × 35.7193 = $71,438,600 - $2,000,000 = $69,438,600
✔✔Calculating the Present Value of a Single Amount for One Period - ✔✔- FV = PV ×
(1 + i )
- PV = FV ÷ (1 + i )
or
PV = FV × [1 ÷ (1 + i )]
✔✔calculating the present value of a single amount for multiple periods - ✔✔PV = FV ×
[1 ÷ (1 + i )2]
✔✔Which statement correctly describes the use of present value interest factors
(PVIFs)?
To find the present value of a sum, you must divide the future value by the PVIF.
For any given time period, as interest rates increase, PVIFs increase.
For any given time period and any given interest rate, PVIFs are always greater than 1.
For any given interest rate, as time increases, PVIF values decrease. - ✔✔To find the
present value, multiply the PVIF by a given future value. For any given time period, as
interest rates increase, PVIFs decrease. For any given time period and any given
interest rate, PVIFs are always less than 1.
✔✔Present Value of an Annuity Due and an Ordinary Annuity - ✔✔The present value of
an annuity, like the future value of an annuity, can be calculated for both an ordinary
annuity and an annuity due. Remember that the payment for an ordinary annuity is
made or received at the end of each annuity period, and that the payment for an annuity
due is made or received at the beginning of each annuity period.
The following time line represents the present value of an ordinary annuity of $100 per
year for three years. Note that, for an ordinary annuity, the valuation date for the present
value occurs at the beginning of the first period, which is one period before the first
payment is made.
✔✔Using PVIFAs: An Ordinary Annuity - ✔✔To calculate how much you need to invest
to provide payments of $1,000 at the end of each year for the next three years, you use
the PVIFA for 3 payments at 5 percent interest, which is 2.723. So the amount you will
need to invest today equals $1,000 × 2.723 = $2,723.00
✔✔Using PVIFAs: An Annuity Due - ✔✔To calculate how much you need to invest to
provide payments of $1,000 at the beginning of each year for the next three years, you
use the PVIFA for 2 payments at 5 percent interest, which is 1.859 and one payment of
$1,000. So the amount you will need to invest today equals ($1,000 × 1.859) + $1,000 =
$1,859 + $1,000 = $2,859.00
, ✔✔Important Insurer Applications of Present Values - ✔✔Insurers use PVIFs and
PVIFAs to determine the prices of one of their most important investments—bonds.
Remember that a bond pays periodic interest payments along with the payment of the
bond's par value upon maturity. So, to determine the price to pay for a bond, an insurer
must calculate two present values:
The present value of the bond's coupon payments, which represents the present value
of an ordinary annuity
The present value of the bond's par value, which is the present value of a single
payment
Future value of an ordinary annuity = periodic payment × FVIFA
Future value of an annuity due = periodic payment × FVIFA for one additional period -
one periodic payment
Present value of an ordinary annuity = periodic payment × PVIFA
Present value of an annuity due = periodic payment × PVIFA for one fewer period + one
periodic payment
✔✔Warwick Financial deposits $1,000,000 in an investment account on the first day of
each year. If Warwick contributes to the account for 6 years and the account earns 4
percent interest annually, what will be the value of the account?
What would we need to find to answer this question?
The future value of an ordinary annuity
The future value of an annuity due
The present value of an ordinary annuity
The present value of an annuity due - ✔✔future value of annuity due- We want to
determine the value of Warwick's money in the future, and because Warwick contributes
to the account at the beginning of the payment period, we need to find the future value
of an annuity due.
✔✔If Jonas Fund puts $1,000,000 in an investment each year on December 31, how
much will Jonas have at the end of 5 years? Assume the account earns 7 percent
interest.
What would we need to find to answer this question?
The future value of an ordinary annuity
The future value of an annuity due
The present value of an ordinary annuity
The present value of an annuity due - ✔✔Future value of an ordinary annuity- In this
situation, we are trying to find the future value of an ordinary annuity. We know this
because we need to determine the amount Jonas will have in the future, and Jonas
makes the investment on the last day of each year.
✔✔Future value of an ordinary annuity
Periodic payment × FVIFA
Periodic payment × FVIFA for one fewer period + one periodic payment
