To calculate the amount of money Liam will have after two years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount of money
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount is $2,000, the annual interest rate is 3% (or 0.03 as a decimal), and interest is compounded annually (so n = 1).
Plugging these values into the formula:
A = 2000(1 + 0.03/1)^(1*2)
A = 2000(1 + 0.03)^2
A = 2000(1.03)^2
A = 2000(1.0609)
A ≈ $2,121.80
Therefore, Liam will have approximately $2,121.80 after two years. Option D, $2,121.80, is the correct answer.
Liam puts $2,000 in the bank with a 3% annual interest rate compounded annuallyIf Liam does not touch his money, how much money will he have after two years? A $2,000,06 B $ 2,060.00 $2,120.00 x D $2,121.80
11 answers
A pencil holder shaped like a triangular prism is shownThe height of the prism is 12 centimeters 10 cm 12 cm 7 cm7 cm What is the lateral surface area of the pencil holder in square centimeters?
To find the lateral surface area of the triangular prism, we need to calculate the sum of the areas of the three rectangular faces.
The two smaller sides will form the base of the triangle, with dimensions of 7 cm and 7 cm.
The longer side will be the height of the prism, which is 12 cm.
To find the area of each rectangular face, we multiply the length and width. For the two smaller sides, the area will be 7 cm * 12 cm = 84 cm².
For the longer side, the area will be 7 cm * 10 cm = 70 cm².
Finally, we add the areas of the three rectangular faces together:
Lateral surface area = 84 cm² + 84 cm² + 70 cm² = 238 cm².
Therefore, the lateral surface area of the pencil holder is 238 square centimeters.
The two smaller sides will form the base of the triangle, with dimensions of 7 cm and 7 cm.
The longer side will be the height of the prism, which is 12 cm.
To find the area of each rectangular face, we multiply the length and width. For the two smaller sides, the area will be 7 cm * 12 cm = 84 cm².
For the longer side, the area will be 7 cm * 10 cm = 70 cm².
Finally, we add the areas of the three rectangular faces together:
Lateral surface area = 84 cm² + 84 cm² + 70 cm² = 238 cm².
Therefore, the lateral surface area of the pencil holder is 238 square centimeters.
Two customers took out loans from a bank Jarrod took out a 5year loan for $4,000 and paid 3.2% annual simple interest Harold took out a 7-year loan for 4,000 and paid 3.9% annual simple interest What is the difference between the amount of interest Jarrod and Harold paid for their loans???
To find the difference between the amount of interest Jarrod and Harold paid for their loans, we need to calculate the interest paid by each individual.
For Jarrod's loan:
Principal amount (P) = $4,000
Interest rate (r) = 3.2% = 0.032 (as a decimal)
Time (t) = 5 years
Simple interest formula:
Interest (I) = P * r * t
I (Jarrod) = $4,000 * 0.032 * 5
I (Jarrod) = $640
For Harold's loan:
Principal amount (P) = $4,000
Interest rate (r) = 3.9% = 0.039 (as a decimal)
Time (t) = 7 years
I (Harold) = $4,000 * 0.039 * 7
I (Harold) = $1,092
The difference between the amount of interest paid by Jarrod and Harold would be:
$1,092 - $640 = $452
Therefore, the difference between the amount of interest Jarrod and Harold paid for their loans is $452.
For Jarrod's loan:
Principal amount (P) = $4,000
Interest rate (r) = 3.2% = 0.032 (as a decimal)
Time (t) = 5 years
Simple interest formula:
Interest (I) = P * r * t
I (Jarrod) = $4,000 * 0.032 * 5
I (Jarrod) = $640
For Harold's loan:
Principal amount (P) = $4,000
Interest rate (r) = 3.9% = 0.039 (as a decimal)
Time (t) = 7 years
I (Harold) = $4,000 * 0.039 * 7
I (Harold) = $1,092
The difference between the amount of interest paid by Jarrod and Harold would be:
$1,092 - $640 = $452
Therefore, the difference between the amount of interest Jarrod and Harold paid for their loans is $452.
Luke deposits $3,500 into each of two savings accounts Account 3simple Account 3% interest compounded annually Luke does not make any additional deposits or withdrawalsWhat is the sum of the balances of Account and at the end of years? 4 A 7,859.28 B$3.920.00 C $3,939.28 D $4,359.28
To calculate the balance of each account at the end of 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount (balance) in the account
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
For Account 1 (with a 3% interest rate compounded annually):
P = $3,500
r = 3% = 0.03 (as a decimal)
n = 1 (compounded annually)
t = 4 years
A1 = $3,500(1 + 0.03/1)^(1*4)
A1 = $3,500(1.03)^4
A1 ≈ $3,921.80
For Account 2 (with a 3% simple interest rate):
P = $3,500
r = 3% = 0.03 (as a decimal)
t = 4 years
A2 = $3,500 + ($3,500 * 0.03 * 4)
A2 = $3,500 + $420
A2 = $3,920
The sum of the balances of both accounts at the end of 4 years would be:
$3,921.80 + $3,920 = $7,841.80
Therefore, the sum of the balances of Account 1 and Account 2 at the end of 4 years is approximately $7,841.80.
None of the given answer choices match this amount exactly, so none of the answer choices are correct.
A = P(1 + r/n)^(nt)
Where:
A = final amount (balance) in the account
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
For Account 1 (with a 3% interest rate compounded annually):
P = $3,500
r = 3% = 0.03 (as a decimal)
n = 1 (compounded annually)
t = 4 years
A1 = $3,500(1 + 0.03/1)^(1*4)
A1 = $3,500(1.03)^4
A1 ≈ $3,921.80
For Account 2 (with a 3% simple interest rate):
P = $3,500
r = 3% = 0.03 (as a decimal)
t = 4 years
A2 = $3,500 + ($3,500 * 0.03 * 4)
A2 = $3,500 + $420
A2 = $3,920
The sum of the balances of both accounts at the end of 4 years would be:
$3,921.80 + $3,920 = $7,841.80
Therefore, the sum of the balances of Account 1 and Account 2 at the end of 4 years is approximately $7,841.80.
None of the given answer choices match this amount exactly, so none of the answer choices are correct.
try again bot
Apologies for the incorrect response earlier. Let's calculate the correct sum of the balances for Account 1 and Account 2 after 4 years:
For Account 1 (with a 3% interest rate compounded annually):
P = $3,500
r = 3% = 0.03 (as a decimal)
n = 1 (compounded annually)
t = 4 years
A1 = P(1 + r/n)^(nt)
A1 = $3,500(1 + 0.03/1)^(1*4)
A1 = $3,500(1.03)^4
A1 ≈ $3,846.09
For Account 2 (with a simple interest rate of 3%):
P = $3,500
r = 3% = 0.03 (as a decimal)
t = 4 years
A2 = P + (P * r * t)
A2 = $3,500 + ($3,500 * 0.03 * 4)
A2 = $3,500 + $420
A2 = $3,920
The sum of the balances of both accounts at the end of 4 years would be:
$3,846.09 + $3,920 = $7,766.09
Therefore, the sum of the balances of Account 1 and Account 2 at the end of 4 years is approximately $7,766.09.
None of the given answer choices match this amount exactly, so none of the answer choices are correct.
For Account 1 (with a 3% interest rate compounded annually):
P = $3,500
r = 3% = 0.03 (as a decimal)
n = 1 (compounded annually)
t = 4 years
A1 = P(1 + r/n)^(nt)
A1 = $3,500(1 + 0.03/1)^(1*4)
A1 = $3,500(1.03)^4
A1 ≈ $3,846.09
For Account 2 (with a simple interest rate of 3%):
P = $3,500
r = 3% = 0.03 (as a decimal)
t = 4 years
A2 = P + (P * r * t)
A2 = $3,500 + ($3,500 * 0.03 * 4)
A2 = $3,500 + $420
A2 = $3,920
The sum of the balances of both accounts at the end of 4 years would be:
$3,846.09 + $3,920 = $7,766.09
Therefore, the sum of the balances of Account 1 and Account 2 at the end of 4 years is approximately $7,766.09.
None of the given answer choices match this amount exactly, so none of the answer choices are correct.
Luke deposits $3,500 into each of two savings accounts Account 3simple Account 3% interest compounded annually Luke does not make any additional deposits or withdrawalsWhat is the sum of the balances of Account and at the end of 4 years?
Apologies for the incorrect response earlier. Let's calculate the correct sum of the balances for Account 1 and Account 2 after 4 years:
For Account 1 (with a simple interest rate of 3%):
P = $3,500
r = 3% = 0.03 (as a decimal)
t = 4 years
A1 = P + (P * r * t)
A1 = $3,500 + ($3,500 * 0.03 * 4)
A1 = $3,500 + $420
A1 = $3,920
For Account 2 (with a 3% interest rate compounded annually):
P = $3,500
r = 3% = 0.03 (as a decimal)
n = 1 (compounded annually)
t = 4 years
A2 = P(1 + r/n)^(nt)
A2 = $3,500(1 + 0.03/1)^(1*4)
A2 = $3,500(1.03)^4
A2 ≈ $3,922.36
The sum of the balances of both accounts at the end of 4 years would be:
$3,920 + $3,922.36 ≈ $7,842.36
Therefore, the sum of the balances of Account 1 and Account 2 at the end of 4 years is approximately $7,842.36.
None of the given answer choices match this amount exactly, but the closest option is B: $3,920.00.
Apologies for any confusion caused.
For Account 1 (with a simple interest rate of 3%):
P = $3,500
r = 3% = 0.03 (as a decimal)
t = 4 years
A1 = P + (P * r * t)
A1 = $3,500 + ($3,500 * 0.03 * 4)
A1 = $3,500 + $420
A1 = $3,920
For Account 2 (with a 3% interest rate compounded annually):
P = $3,500
r = 3% = 0.03 (as a decimal)
n = 1 (compounded annually)
t = 4 years
A2 = P(1 + r/n)^(nt)
A2 = $3,500(1 + 0.03/1)^(1*4)
A2 = $3,500(1.03)^4
A2 ≈ $3,922.36
The sum of the balances of both accounts at the end of 4 years would be:
$3,920 + $3,922.36 ≈ $7,842.36
Therefore, the sum of the balances of Account 1 and Account 2 at the end of 4 years is approximately $7,842.36.
None of the given answer choices match this amount exactly, but the closest option is B: $3,920.00.
Apologies for any confusion caused.