MATH 110 Sec 8-4: Annuities
Practice Exercises
Monthly payments of $75 are paid into an annuity
beginning on January 31 with a yearly interest rate of
9% compounded monthly. What is the total value of
the annuity on September 1 (round to nearest cent).
MATH 110 Sec 8-4: Annuities
Practice Exercises
Monthly payments of $75 are paid into an annuity
beginning on January 31 with a yearly interest rate of
9% compounded monthly. What is the total value of
the annuity on September 1 (round to nearest cent).
First note that payments on an ordinary annuity are made at the end of
each month so, by Sep 1, there are a total of 8 monthly payments.
MATH 110 Sec 8-4: Annuities
Practice Exercises
Monthly payments of $75 are paid into an annuity
beginning on January 31 with a yearly interest rate of
9% compounded monthly. What is the total value of
the annuity on September 1 (round to nearest cent).
First note that payments on an ordinary annuity are made at the end of
each month so, by Sep 1, there are a total of 8 monthly payments.
8
2
Also remember that t MUST be in years. So, 8 months is 𝑡 = 12 = 3 year.
MATH 110 Sec 8-4: Annuities
Practice Exercises
Monthly payments of $75 are paid into an annuity
beginning on January 31 with a yearly interest rate of
9% compounded monthly. What is the total value of
the annuity on September 1 (round to nearest cent).
𝐴=𝑅
1+𝑖 𝑛 −1
𝑖
where 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑚𝑡
2
3
(and 𝑡 = )
MATH 110 Sec 8-4: Annuities
Practice Exercises
Find the value of the ordinary annuity at the end of
the indicated time period (to nearest cent). The
frequency of deposits is the same as the frequency of
compounding. Amount: $1000, 5.5% quarterly, 8 yrs
MATH 110 Sec 8-4: Annuities
Practice Exercises
Find the value of the ordinary annuity at the end of
the indicated time period (to nearest cent). The
frequency of deposits is the same as the frequency of
compounding. Amount: $1000, 5.5% quarterly, 8 yrs
𝐴=𝑅
1+𝑖 𝑛 −1
𝑖
where 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑚𝑡
MATH 110 Sec 8-4: Annuities
Practice Exercises
Kal wants to save $15,000 in 6 years with monthly
payments to an ordinary annuity for a down payment
on a condo at the beach. If the annuity pays 0.6%
monthly interest, what will his monthly payment be?
(Round answer UP to the nearest cent.)
MATH 110 Sec 8-4: Annuities
Practice Exercises
Kal wants to save $15,000 in 6 years with monthly
payments to an ordinary annuity for a down payment
on a condo at the beach. If the annuity pays 0.6%
monthly interest, what will his monthly payment be?
(Round answer UP to the nearest cent.)
𝐴=𝑅
1+𝑖 𝑛 −1
𝑖
where 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑚𝑡
MATH 110 Sec 8-4: Annuities
Practice Exercises
Kal wants to save $15,000 in 6 years with monthly
payments to an ordinary annuity for a down payment
on a condo at the beach. If the annuity pays 0.6%
monthly interest, what will his monthly payment be?
(Round answer UP to the nearest cent.)
𝐴
1+𝑖 𝑛 −1
𝑖
𝑟
=𝑅
where 𝑖 = and 𝑛 = 𝑚𝑡
𝑚
BE CAREFUL!
We are accustomed to being given r (the ANNUAL interest rate).
But here we are given i (the MONTHLY interest rate) instead.
MATH 110 Sec 8-4: Annuities
Practice Exercises
Kal wants to save $15,000 in 6 years with monthly
payments to an ordinary annuity for a down payment
on a condo at the beach. If the annuity pays 0.6%
monthly interest, what will his monthly payment be?
(Round answer UP to the nearest cent.)
𝐴
1+𝑖 𝑛 −1
𝑖
𝑟
=𝑅
where 𝑖 = and 𝑛 = 𝑚𝑡
𝑚
BE CAREFUL!
We are accustomed to being given r (the ANNUAL interest rate).
But here we are given i (the MONTHLY interest rate) instead.
So, the problem tells us directly that 𝑖 = 0.6% = 0.006
MATH 110 Sec 8-4: Annuities
Practice Exercises
Kal wants to save $15,000 in 6 years with monthly
payments to an ordinary annuity for a down payment
on a condo at the beach. If the annuity pays 0.6%
monthly interest, what will his monthly payment be?
(Round answer UP to the nearest cent.)
𝐴=𝑅
1+𝑖 𝑛 −1
𝑖
where 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑚𝑡
so
𝑖 = 0.006
MATH 110 Sec 8-4: Annuities
Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). Max begins at age 41 saving
$2400 per year in the same type of account until age 65 (25
payments). How much does each have in his account at age
65? (Round answers to the nearest cent.)
MATH 110 Sec 8-4: Annuities
Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). Max begins at age 41 saving
$2400 per year in the same type of account until age 65 (25
payments). How much does each have in his account at age
65? (Round answers to the nearest cent.)
The case of Max is simpler so let’s do it first.
MATH 110 Sec 8-4: Annuities
Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). Max begins at age 41 saving
$2400 per year in the same type of account until age 65 (25
payments). How much does each have in his account at age
65? (Round answers to the nearest cent.)
The case of Max is simpler so let’s do it first.
1+𝑖 𝑛 −1
𝑟
𝐴=𝑅
𝑖
where 𝑖 =
𝑚
and 𝑛 = 𝑚𝑡
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). Max begins at age 41 saving
$2400 per year in the same type of account until age 65 (25
payments). How much does each have in his account at age
65? (Round answers to the nearest cent.)
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). Max begins at age 41 saving
$2400 per year in the same type of account until age 65 (25
payments). How much does each have in his account at age
65? (Round answers to the nearest cent.)
Now let’s look at Julio’s case.
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). (Round to the nearest cent.)
Now let’s look at Julio’s case.
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). (Round to the nearest cent.)
Now let’s look at Julio’s case.
1+𝑖 𝑛 −1
𝐴=𝑅
𝑖
where 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑚𝑡
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). (Round to the nearest cent.)
So, after 15 years, Julio has A = $31,342.03764 in his account.
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). (Round to the nearest cent.)
So, after 15 years, Julio has A = $31,342.03764 in his account.
But now, Julio just lets that money sit in the account
for 30 more years with no more periodic payments.
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). (Round to the nearest cent.)
So, after 15 years, Julio has A = $31,342.03764 in his account.
But now, Julio just lets that money sit in the account
for 30 more years with no more periodic payments.
This means for the last 30 years, this account is
just an ordinary compound interest account.
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). (Round to the nearest cent.)
So, after 15 years, Julio has A = $31,342.03764 in his account.
But now, Julio just lets that money sit in the account
for 30 more years with no more periodic payments.
This means for the last 30 years, this account is
just an ordinary compound interest account.
𝐴 =𝑃 1+𝑖
𝑛
where 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑚𝑡
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). (Round to the nearest cent.)
So, after 15 years, Julio has A = $31,342.03764 in his account.
This means for the last 30 years, this account is
just an ordinary compound interest account.
𝐴 =𝑃 1+𝑖
𝑛
where 𝑖 =
𝑟
𝑚
and 𝑛 = 𝑚𝑡
MATH 110 Sec 8-4: Annuities
So for Max, 𝐴 =$163,146.87 Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs (Round to the nearest cent.)
and for Julio, 𝐴 =$274,398.14
MATH 110 Sec 8-4: Annuities
Practice Exercises
At age 21 Julio begins saving $1200 each year until age 35
(15 payments) in an ordinary annuity paying 7.5% annual
interest compounded yearly and then leaves his money in the
account until age 65 (30 yrs). Max begins at age 41 saving
$2400 per year in the same type of account until age 65 (25
payments). How much does each have in his account at age
65? (Round answers to the nearest cent.)
So for Max, 𝐴 =$163,146.87
and for Julio, 𝐴 =$274,398.14