Mathematics: Jason invests $1000 at a bank that offers 3% interest compounded annually. Write an equation to

Jason invests $1000 at a bank that offers 3%, №9217429, 24.07.2022 10:15

Advanced Placement (AP)

Worth 75-100 points you must answer each question and show your math tyler has $1000 that he wants to put in a savings account. he wants to save the money for 6 years. after 6 years he plans to take the money out and spend it on college. he looks at two different banks, and they offer him different interest options. 1. bank a offers tyler 4% simple interest. how much would tyler’s investment be worth after 6 years in this account? show your calculations below. 2. bank b offers tyler 3% interest compounded annually. how much would tyler’s investment

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P Answered by PhD

9

TYLER

1. Bank A: $1240

2. Bank B: $1194.05

3. Choose Bank A, simple interest at higher rate

TYLER'S MOM

1. Bank A: $2200

2. Bank B: $2427.26

3. Choose Bank B, compound interest at lower rate

4. The simple interest rate at 4% is better for Tyler, but the compound interest rate at 3% is better for Tyler's mom. Simple interest is calculated on the principal. Compound interest is calculated on the principal and the other interest that was earned. Over a longer period of time, the investment worth after compound interest will be worth more, even if the interest rate is lower. Since Tyler's mom has more time for her investment than Tyler, compound interest at a lower rate is more advantageous to her.

Explanation:

For this problem, you need the formula to calculate amount after simple interest A = P(1 + rt)

"A" for amount (final worth of investment)

"P" for principal (starting investment)

"r" for interest rate in decimal form

"t" for time in years

You also need the formula for amount after compound interest A = P(1 + i)ⁿ

"A" for amount

"P" for principal

"i" for interest per compounding period, calculated using i = r/c

"n" for number of compounding periods, calculated by n = tc

"c" means how often interest is calculated. (Ex: annually = 1; quarterly = 4)

To solve the problems, substitute the known values into the equations.

FOR TYLER: P = 1000; t = 6

1. Use simple interest formula. r = 4% = 0.04 (converted to decimals)

A = P(1 + rt)

A = 1000(1 + (0.04)(6)) Substituted known values

A = 1000(1 + 0.24) Solved multiplication within brackets

A = 1000(1.24) Solved addition within brackets

A = 1240 Bank A future investment worth

Tyler's investment would be worth $1240 in Bank A.

2. Use compound interest formula. r = 3% = 0.03 (converted to decimals)

Calculate "i" and "n" inside the formula.

$A = P(1 + i)^{n}$

$A = 1000(1 + (\frac{r}{c}))^{tc}$ c = 1 because interest is calculated annually

$A = 1000(1 + 0.03)^{6}$ Substituted known values.

$A = 1000(1.03)^{6}$ Solved within brackets first.

A = 1194.05 Rounded 1194.0523 to two decimal places

Tyler's investment would be worth $1194.05 in Bank B.

3. Tyler should place the $1000 he is saving for college in Bank A because he will have more money.

Bank A > Bank B

1240 > 1194.05

FOR TYLER'S MOM P = 1000; t = 30

1. Use simple interest formula. r = 4% = 0.04 (converted to decimals)

A = P(1 + rt)

A = 1000(1 + (0.04)(30)) Substituted known values

A = 1000(1 + 1.2) Solved multiplication within brackets first

A = 1000(2.2) Solved addition within brackets

A = 2200

Tyler's mom's investment would be worth $2200 from Bank A.

2. Use compound interest formula. r = 3% = 0.03 (converted to decimals)

Calculate "i" and "n" inside the formula.

$A = P(1 + i)^{n}$

$A = 1000(1 + (\frac{r}{c}))^{tc}$ c = 1 because interest is calculated annually

$A = 1000(1 + 0.03)^{30}$ Substituted known values

$A = 1000(1.03)^{30}$ Solved within brackets first

A = 2427.26 Rounded 2427.26247 to two decimal places

Tyler's mom's investment would be worth $2427.26 from Bank B.

3. Tyler's mom should place the $1000 she is saving for retirement in Bank B because she will have more money.

Bank A < Bank B

2200 < 2427.26

4. The simple interest rate at 4% is better for Tyler, but the compound interest rate at 3% is better for Tyler's mom. Simple interest is calculated on the principal. Compound interest is calculated on the principal and the other interest that was earned. Over a longer period of time, the investment worth after compound interest will be worth more, even if the interest rate is lower. Since Tyler's mom has more time for her investment than Tyler, compound interest at a lower rate is more advantageous to her.

Mathematics

30 points, and brainliest tyler has $1000 that he wants to put in a savings account. he wants to save the money for 6 years. after 6 years he plans to take the money out and spend it on college. he looks at two different banks, and they offer him different interest options. (i ve already solved bank a which is $1,240) bank b offers tyler 3% interest compounded annually. how much would tyler’s investment be worth after 6 years in this account? show your calculations below. tyler’s mom also has $1000 that she wants to put in a savings account. she

Step-by-step answer

P Answered by Specialist

4

Tyler Bank B: $1,180: Mom Bank A: $2,200: Mom Bank B: $1,900

Step-by-step explanation: Look at Picture

Mathematics

30 points, and brainliest tyler has $1000 that he wants to put in a savings account. he wants to save the money for 6 years. after 6 years he plans to take the money out and spend it on college. he looks at two different banks, and they offer him different interest options. (i ve already solved bank a which is $1,240) bank b offers tyler 3% interest compounded annually. how much would tyler’s investment be worth after 6 years in this account? show your calculations below. tyler’s mom also has $1000 that she wants to put in a savings account. she

Step-by-step answer

P Answered by Master

4

Tyler Bank B: $1,180: Mom Bank A: $2,200: Mom Bank B: $1,900

Step-by-step explanation: Look at Picture

Mathematics

Lease tyler has $1000 that he wants to put in a savings account. he wants to save the money for 6 years. after 6 years he plans to take the money out and spend it on college. he looks at two different banks, and they offer him different interest options. bank a offers tyler 4% simple interest. how much would tyler’s investment be worth after 6 years in this account? show your calculations below. bank b offers tyler 3% interest compounded annually. how much would tyler’s investment be worth after 6 years in this account? show your calculations below.

Step-by-step answer

P Answered by PhD

6

Bank A = 1000 x (1 + (0.04*6)) = $1,240

Bank B = 1000 x (1+0.03)^6 = $1,194.05

Bank A would be worth more

Mathematics

Lease tyler has $1000 that he wants to put in a savings account. he wants to save the money for 6 years. after 6 years he plans to take the money out and spend it on college. he looks at two different banks, and they offer him different interest options. bank a offers tyler 4% simple interest. how much would tyler’s investment be worth after 6 years in this account? show your calculations below. bank b offers tyler 3% interest compounded annually. how much would tyler’s investment be worth after 6 years in this account? show your calculations below.

Step-by-step answer

P Answered by PhD

6

Bank A = 1000 x (1 + (0.04*6)) = $1,240

Bank B = 1000 x (1+0.03)^6 = $1,194.05

Bank A would be worth more

Mathematics

Imran is paid ?286 per week Every week he puts 20% of his wage into a savings account How much does he put into his savings each week

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P Answered by PhD

The answer is in the image

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

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P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

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An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?

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P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45

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