Math / Numbers & Operations

Question9 Multiple Choice 6 points
Assume $\$ 20,000$ is deposited into a savings account. Boulder Bank offers an annual rate of $0.84 \%$ for 5 years. Stone Bank offers a rate of $3.7 \%$ interest for 1 year. Which earns more interest? Boulder Bank Stone Bank 10 Fill in the Blank 6 points
A couple is planning a savings account for a newborn baby. They start with $\$ 10,700$ they received as cash gifts. If no deposits or withdrawals are made, what is the balance of the account if it earns $0.98 \%$ interest for 18 years? type your answer... 11 Fill in the Blank 6 points
Ron estimates it will cost him $\$ 600,000$ to send his daughter to a private college in 18 years. He currently has $\$ 130,000$ to deposit in an account. What simple interest rate must his account have to reach a balance of $\$ 600,000$ in 18 years? Round to the nearest percent. type your answer... Submit

Studdy Solution

STEP 1

1. Boulder Bank offers an annual interest rate of $0.84\%$ for 5 years.
2. Stone Bank offers an annual interest rate of $3.7\%$ for 1 year.
3. Interest is calculated using simple interest unless otherwise specified.
4. The initial deposit for Boulder Bank and Stone Bank is $\$20,000$ .
5. For the newborn's savings account, the initial deposit is $\$10,700$ with an interest rate of $0.98\%$ for 18 years.
6. Ron needs $\$600,000$ in 18 years, starting with $\$130,000$ .

STEP 2

1. Calculate interest earned at Boulder Bank.
2. Calculate interest earned at Stone Bank.
3. Compare the interest earned by both banks.
4. Calculate the future balance of the newborn's savings account.
5. Determine the required interest rate for Ron's savings.

STEP 3

Calculate the interest earned at Boulder Bank using simple interest formula $I = P \times r \times t$ .
$I = 20000 \times \frac{0.84}{100} \times 5$

STEP 4

Perform the calculation for Boulder Bank.
$I = 20000 \times 0.0084 \times 5 = 840$

STEP 5

Calculate the interest earned at Stone Bank using simple interest formula $I = P \times r \times t$ .
$I = 20000 \times \frac{3.7}{100} \times 1$

STEP 6

Perform the calculation for Stone Bank.
$I = 20000 \times 0.037 \times 1 = 740$

STEP 7

Compare the interest earned by Boulder Bank and Stone Bank.
Boulder Bank earns $\$840$ and Stone Bank earns $\$740$ .

STEP 8

Calculate the future balance of the newborn's savings account using simple interest formula $A = P + I$ .
$I = 10700 \times \frac{0.98}{100} \times 18$

STEP 9

Perform the calculation for the newborn's savings account.
$I = 10700 \times 0.0098 \times 18 = 1888.44$
$A = 10700 + 1888.44 = 12588.44$

STEP 10

Determine the required interest rate for Ron's savings using the formula $A = P(1 + rt)$ .
$600000 = 130000(1 + r \times 18)$

STEP 11

Solve for $r$ .
$600000 = 130000 + 130000 \times r \times 18$
$470000 = 130000 \times r \times 18$
$r = \frac{470000}{130000 \times 18}$
$r \approx 0.20085$

STEP 12

Convert $r$ to a percentage and round to the nearest percent.
$r \approx 20.085\% \approx 20\%$
The answers are:
1. Boulder Bank earns more interest: $\$840$ .
2. The balance of the newborn's savings account: $\$12588.44$ .
3. Required interest rate for Ron's savings: $20\%$ .

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Calculate interest earned at Boulder Bank.
2. Calculate interest earned at Stone Bank.
3. Compare the interest earned by both banks.
4. Calculate the future balance of the newborn's savings account.
5. Determine the required interest rate for Ron's savings.

STEP 3

Calculate the interest earned at Boulder Bank using simple interest formula $I = P \times r \times t$ .
$I = 20000 \times \frac{0.84}{100} \times 5$

STEP 4

Perform the calculation for Boulder Bank.
$I = 20000 \times 0.0084 \times 5 = 840$

STEP 5

Calculate the interest earned at Stone Bank using simple interest formula $I = P \times r \times t$ .
$I = 20000 \times \frac{3.7}{100} \times 1$

STEP 6

Perform the calculation for Stone Bank.
$I = 20000 \times 0.037 \times 1 = 740$

STEP 7

Compare the interest earned by Boulder Bank and Stone Bank.
Boulder Bank earns $\$840$ and Stone Bank earns $\$740$ .

STEP 8

Calculate the future balance of the newborn's savings account using simple interest formula $A = P + I$ .
$I = 10700 \times \frac{0.98}{100} \times 18$

STEP 9

Perform the calculation for the newborn's savings account.
$I = 10700 \times 0.0098 \times 18 = 1888.44$
$A = 10700 + 1888.44 = 12588.44$

STEP 10

Determine the required interest rate for Ron's savings using the formula $A = P(1 + rt)$ .
$600000 = 130000(1 + r \times 18)$

STEP 11

Solve for $r$ .
$600000 = 130000 + 130000 \times r \times 18$
$470000 = 130000 \times r \times 18$
$r = \frac{470000}{130000 \times 18}$
$r \approx 0.20085$

STEP 12

Convert $r$ to a percentage and round to the nearest percent.
$r \approx 20.085\% \approx 20\%$
The answers are:
1. Boulder Bank earns more interest: $\$840$ .
2. The balance of the newborn's savings account: $\$12588.44$ .
3. Required interest rate for Ron's savings: $20\%$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

1. Calculate interest earned at Boulder Bank.2. Calculate interest earned at Stone Bank.3. Compare the interest earned by both banks.4. Calculate the future balance of the newborn's savings account.5. Determine the required interest rate for Ron's savings.

STEP 3

Calculate the interest earned at Boulder Bank using simple interest formula I=P×r×tI = P \times r \times tI=P×r×t.I=20000×0.84100×5I = 20000 \times \frac{0.84}{100} \times 5I=20000×1000.84​×5

STEP 4

Perform the calculation for Boulder Bank.I=20000×0.0084×5=840I = 20000 \times 0.0084 \times 5 = 840I=20000×0.0084×5=840

STEP 5

Calculate the interest earned at Stone Bank using simple interest formula I=P×r×tI = P \times r \times tI=P×r×t.I=20000×3.7100×1I = 20000 \times \frac{3.7}{100} \times 1I=20000×1003.7​×1

STEP 6

Perform the calculation for Stone Bank.I=20000×0.037×1=740I = 20000 \times 0.037 \times 1 = 740I=20000×0.037×1=740

STEP 7

Compare the interest earned by Boulder Bank and Stone Bank.Boulder Bank earns $840\$840$840 and Stone Bank earns $740\$740$740.

STEP 8

Calculate the future balance of the newborn's savings account using simple interest formula A=P+IA = P + IA=P+I.I=10700×0.98100×18I = 10700 \times \frac{0.98}{100} \times 18I=10700×1000.98​×18

STEP 9

Perform the calculation for the newborn's savings account.I=10700×0.0098×18=1888.44I = 10700 \times 0.0098 \times 18 = 1888.44I=10700×0.0098×18=1888.44A=10700+1888.44=12588.44A = 10700 + 1888.44 = 12588.44A=10700+1888.44=12588.44

STEP 10

Determine the required interest rate for Ron's savings using the formula A=P(1+rt)A = P(1 + rt)A=P(1+rt).600000=130000(1+r×18)600000 = 130000(1 + r \times 18)600000=130000(1+r×18)

STEP 11

Solve for rrr.600000=130000+130000×r×18600000 = 130000 + 130000 \times r \times 18600000=130000+130000×r×18470000=130000×r×18470000 = 130000 \times r \times 18470000=130000×r×18r=470000130000×18r = \frac{470000}{130000 \times 18}r=130000×18470000​r≈0.20085r \approx 0.20085r≈0.20085

STEP 12

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Calculate interest earned at Boulder Bank.
2. Calculate interest earned at Stone Bank.
3. Compare the interest earned by both banks.
4. Calculate the future balance of the newborn's savings account.
5. Determine the required interest rate for Ron's savings.

Calculate the interest earned at Boulder Bank using simple interest formula $I = P \times r \times t$ .
$I = 20000 \times \frac{0.84}{100} \times 5$

Perform the calculation for Boulder Bank.
$I = 20000 \times 0.0084 \times 5 = 840$

Calculate the interest earned at Stone Bank using simple interest formula $I = P \times r \times t$ .
$I = 20000 \times \frac{3.7}{100} \times 1$

Perform the calculation for Stone Bank.
$I = 20000 \times 0.037 \times 1 = 740$

Compare the interest earned by Boulder Bank and Stone Bank.
Boulder Bank earns $\$840$ and Stone Bank earns $\$740$ .

Calculate the future balance of the newborn's savings account using simple interest formula $A = P + I$ .
$I = 10700 \times \frac{0.98}{100} \times 18$

Perform the calculation for the newborn's savings account.
$I = 10700 \times 0.0098 \times 18 = 1888.44$
$A = 10700 + 1888.44 = 12588.44$

Determine the required interest rate for Ron's savings using the formula $A = P(1 + rt)$ .
$600000 = 130000(1 + r \times 18)$

Solve for $r$ .
$600000 = 130000 + 130000 \times r \times 18$
$470000 = 130000 \times r \times 18$
$r = \frac{470000}{130000 \times 18}$
$r \approx 0.20085$