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Math Problems
Grade 7
Compound interest
Emma is saving money and plans on making monthly contributions into an account earning a monthly interest rate of
0.475
%
0.475 \%
0.475%
. If Emma would like to end up with
$
14
,
000
\$ 14,000
$14
,
000
after
14
14
14
months, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Emily is saving money and plans on making monthly contributions into an account earning a monthly interest rate of
0.375
%
0.375 \%
0.375%
. If Emily would like to end up with
$
4
,
000
\$ 4,000
$4
,
000
after
13
13
13
months, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Julian is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of
1.875
%
1.875 \%
1.875%
. If Julian would like to end up with
$
17
,
000
\$ 17,000
$17
,
000
after
10
10
10
years, how much does he need to contribute to the account every quarter, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Rashon is saving money and plans on making monthly contributions into an account earning an annual interest rate of
3.9
%
3.9 \%
3.9%
compounded monthly. If Rashon would like to end up with
$
144
,
000
\$ 144,000
$144
,
000
after
10
10
10
years, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Charlotte is saving money and plans on making monthly contributions into an account earning an annual interest rate of
3
%
3 \%
3%
compounded monthly. If Charlotte would like to end up with
$
61
,
000
\$ 61,000
$61
,
000
after
9
9
9
years, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Layla is saving money and plans on making monthly contributions into an account earning an annual interest rate of
5.7
%
5.7 \%
5.7%
compounded monthly. If Layla would like to end up with
$
113
,
000
\$ 113,000
$113
,
000
after
14
14
14
years, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Morgan is saving money and plans on making monthly contributions into an account earning a monthly interest rate of
0.75
%
0.75 \%
0.75%
. If Morgan would like to end up with
$
99
,
000
\$ 99,000
$99
,
000
after
10
10
10
years, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Christopher is saving money and plans on making monthly contributions into an account earning a monthly interest rate of
0.5
%
0.5 \%
0.5%
. If Christopher would like to end up with
$
29
,
000
\$ 29,000
$29
,
000
after
12
12
12
years, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Rashaad is saving money and plans on making monthly contributions into an account earning an annual interest rate of
8.4
%
8.4 \%
8.4%
compounded monthly. If Rashaad would like to end up with
$
75
,
000
\$ 75,000
$75
,
000
after
8
8
8
years, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Charlotte is saving money and plans on making monthly contributions into an account earning a monthly interest rate of
0.7
%
0.7 \%
0.7%
. If Charlotte would like to end up with
$
13
,
000
\$ 13,000
$13
,
000
after
35
35
35
months, how much does she need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Nicole is saving money and plans on making quarterly contributions into an account earning an annual interest rate of
3.1
%
3.1 \%
3.1%
compounded quarterly. If Nicole would like to end up with
$
31
,
000
\$ 31,000
$31
,
000
after
11
11
11
years, how much does she need to contribute to the account every quarter, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
Francisco is saving money and plans on making quarterly contributions into an account earning a quarterly interest rate of
1.45
%
1.45 \%
1.45%
. If Francisco would like to end up with
$
48
,
000
\$ 48,000
$48
,
000
after
12
12
12
years, how much does he need to contribute to the account every quarter, to the nearest dollar? Use the following formula to determine your answer.
\newline
A
=
d
(
(
1
+
i
)
n
−
1
i
)
A=d\left(\frac{(1+i)^{n}-1}{i}\right)
A
=
d
(
i
(
1
+
i
)
n
−
1
)
\newline
A
=
A=
A
=
the future value of the account after
n
n
n
periods
\newline
d
=
d=
d
=
the amount invested at the end of each period
\newline
i
=
i=
i
=
the interest rate per period
\newline
n
=
n=
n
=
the number of periods
\newline
Answer:
Get tutor help
A person places
$
3370
\$ 3370
$3370
in an investment account earning an annual rate of
9
%
9 \%
9%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in t years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
16
16
16
years.
\newline
Answer:
Get tutor help
A person places
$
634
\$ 634
$634
in an investment account earning an annual rate of
6.4
%
6.4 \%
6.4%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in
t
t
t
years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
13
13
13
years.
\newline
Answer:
Get tutor help
A person places
$
8230
\$ 8230
$8230
in an investment account earning an annual rate of
4.1
%
4.1 \%
4.1%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in
t
t
t
years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
15
15
15
years.
\newline
Answer:
Get tutor help
A person places
$
70500
\$ 70500
$70500
in an investment account earning an annual rate of
9
%
9 \%
9%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in
t
t
t
years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
7
7
7
years.
\newline
Answer:
Get tutor help
A person places
$
43900
\$ 43900
$43900
in an investment account earning an annual rate of
9.2
%
9.2 \%
9.2%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in t years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
19
19
19
years.
\newline
Answer:
Get tutor help
A person places
$
78800
\$ 78800
$78800
in an investment account earning an annual rate of
7.4
%
7.4 \%
7.4%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in
t
t
t
years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
3
3
3
years.
\newline
Answer:
Get tutor help
A person places
$
52300
\$ 52300
$52300
in an investment account earning an annual rate of
7.5
%
7.5 \%
7.5%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in t years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
7
7
7
years.
\newline
Answer:
Get tutor help
A person places
$
73100
\$ 73100
$73100
in an investment account earning an annual rate of
7.1
%
7.1 \%
7.1%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in
t
t
t
years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
6
6
6
years.
\newline
Answer:
Get tutor help
A person places
$
6520
\$ 6520
$6520
in an investment account earning an annual rate of
7.7
%
7.7 \%
7.7%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in t years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
14
14
14
years.
\newline
Answer:
Get tutor help
A person places
$
4290
\$ 4290
$4290
in an investment account earning an annual rate of
3.7
%
3.7 \%
3.7%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in
t
t
t
years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
2
2
2
years.
\newline
Answer:
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A person places
$
427
\$ 427
$427
in an investment account earning an annual rate of
3.7
%
3.7 \%
3.7%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in t years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
16
16
16
years.
\newline
Answer:
Get tutor help
A person places
$
118
\$ 118
$118
in an investment account earning an annual rate of
3.3
%
3.3 \%
3.3%
, compounded continuously. Using the formula
V
=
P
e
r
t
V=P e^{r t}
V
=
P
e
r
t
, where
V
\mathrm{V}
V
is the value of the account in
t
t
t
years,
P
\mathrm{P}
P
is the principal initially invested,
e
\mathrm{e}
e
is the base of a natural logarithm, and
r
r
r
is the rate of interest, determine the amount of money, to the nearest cent, in the account after
9
9
9
years.
\newline
Answer:
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Victoria bought stock in a company two years ago that was worth
x
x
x
dollars. During the first year that she owned the stock, it decreased by
16
%
16 \%
16%
. During the second year the value of the stock increased by
8
%
8 \%
8%
. Write an expression in terms of
x
x
x
that represents the value of the stock after the two years have passed.
\newline
Answer:
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Cai goes to a store and buys an item that costs
x
x
x
dollars. He has a coupon for
10
%
10 \%
10%
off, and then a
5
%
5 \%
5%
tax is added to the discounted price. Write an expression in terms of
x
x
x
that represents the total amount that Cai paid at the register.
\newline
Answer:
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Malika bought stock in a company two years ago that was worth
x
x
x
dollars. During the first year that she owned the stock, it increased by
28
%
28 \%
28%
. During the second year the value of the stock increased by
25
%
25 \%
25%
. Write an expression in terms of
x
x
x
that represents the value of the stock after the two years have passed.
\newline
Answer:
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Camila bought stock in a company two years ago that was worth
x
x
x
dollars. During the first year that she owned the stock, it decreased by
19
%
19 \%
19%
. During the second year the value of the stock decreased by
8
%
8 \%
8%
. Write an expression in terms of
x
x
x
that represents the value of the stock after the two years have passed.
\newline
Answer:
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Fatoumata bought stock in a company two years ago that was worth
x
x
x
dollars. During the first year that she owned the stock, it increased by
30
%
30 \%
30%
. During the second year the value of the stock decreased by
22
%
22 \%
22%
. Write an expression in terms of
x
x
x
that represents the value of the stock after the two years have passed.
\newline
Answer:
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Ebuka's monthly rent is
$
750
\$750
$750
. If Ebuka pays the rent late, his landlord charges
4
%
4\%
4%
interest per week that the payment is late. Write a function that gives the total cost
R
(
t
)
R(t)
R
(
t
)
, in dollars, of Ebuka's rent if he pays it
t
t
t
weeks late.
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The present value (PV) of an investment is the amount that should be invested today at a specified interest rate in order to earn a certain amount at a future date. The amount desired is called the future value. For a future value of
$
10
,
000
\$10,000
$10
,
000
, which of the following functions models the present value,
P
V
PV
P
V
, to be invested in a savings account earning
5
%
5\%
5%
interest compounded annually for
t
t
t
years?
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The rate of change
d
P
d
t
\frac{d P}{d t}
d
t
d
P
of the number of students who heard a rumor is modeled by the following differential equation:
\newline
d
P
d
t
=
8580
94019
P
(
1
−
P
780
)
\frac{d P}{d t}=\frac{8580}{94019} P\left(1-\frac{P}{780}\right)
d
t
d
P
=
94019
8580
P
(
1
−
780
P
)
\newline
At
t
=
0
t=0
t
=
0
, the number of students who heard the rumor is
149
149
149
and is increasing at a rate of
11
11
11
students per hour. Find
lim
t
→
∞
P
′
(
t
)
\lim _{t \rightarrow \infty} P^{\prime}(t)
lim
t
→
∞
P
′
(
t
)
.
\newline
Answer:
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Shota invests
$
1000
\$ 1000
$1000
in a certificate of deposit that earns interest. The investment's value is multiplied by
1
1
1
.
02
02
02
each year.
\newline
Which expression gives the investment's value after
5
5
5
years?
\newline
Choose
1
1
1
answer:
\newline
(A)
1000
⋅
1.0
2
5
1000 \cdot 1.02^{5}
1000
⋅
1.0
2
5
\newline
(B)
1000
⋅
(
1
+
1.02
)
5
1000 \cdot(1+1.02)^{5}
1000
⋅
(
1
+
1.02
)
5
\newline
(C)
1000
+
(
1
+
1.02
)
5
1000+(1+1.02)^{5}
1000
+
(
1
+
1.02
)
5
\newline
(D)
1000
+
1.0
2
5
1000+1.02^{5}
1000
+
1.0
2
5
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