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Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.
Q. From the choices below, identify the amount Customer 1 will have in Clearwater State Bank after one year, and the amount Customer 1 will have after 21 months if he moves his balance at the end of the first year to Clearwater Credit Union. Make two selections.
Q. From the choices below, identify the amount Customer 1 will have in Clearwater State Bank after one year, and the amount Customer 1 will have after 21 months if he moves his balance at the end of the first year to Clearwater Credit Union. Make two selections.
- a)121
- b)135
- c)168
- d)186
- e)220
Correct answer is option 'A,B'. Can you explain this answer?
Verified Answer
Clearwater State Bank is offering an introductory 20% interest rate on...
The correct answers are 121 and 135. Customer 1 is placing $100 in Clearwater State Bank for one year only, so it will compound twice at 10%. Remember that 20% interest compounded semi-annually is the same as 10% interest compounded every six months. That will give the customer $100 x 1.1 = $110 after six months, and $110 x 1.1 = $121 after one year. Customer 1 then takes that $121 and places it in the Clearwater Credit Union for the remaining 9 months out of the 21 months total (12 months was the first year at the Clearwater State Bank). At Clearwater Credit Unit, the $121 will compound 4 times at 3.75% every quarter. After three months that will be $121 * 1.0375 = $125.54. After six months that will be $125.54 * 1.0375 = $130.25. After nine months that will be approximately $135.13, or $135.
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Clearwater State Bank is offering an introductory 20% interest rate on...
Customer 1's Savings with Clearwater State Bank:
Customer 1 deposits $100 in Clearwater State Bank account. The interest rate for the first year is 20% compounded semi-annually.
Amount after one year:
The interest will compound semi-annually, which means it will be applied twice in a year. The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $100
r = 20% = 0.2
n = 2 (compounded semi-annually)
t = 1 year
Plugging in these values into the formula, we get:
A = 100(1 + 0.2/2)^(2*1)
A = 100(1 + 0.1)^2
A = 100(1.1)^2
A = 100(1.21)
A = $121
So after one year, Customer 1 will have $121 in the Clearwater State Bank account.
Amount after 21 months:
After one year, Customer 1 decides to move his balance to Clearwater Credit Union. He will have $121 at this point. Clearwater Credit Union offers an interest rate of 15% compounded quarterly for the first year.
To calculate the amount after 21 months, we need to calculate the interest for the remaining 9 months (21 - 12 months).
Amount after 9 months:
The interest will compound quarterly, which means it will be applied four times in a year. The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $121
r = 15% = 0.15
n = 4 (compounded quarterly)
t = 9/12 year (9 months)
Plugging in these values into the formula, we get:
A = 121(1 + 0.15/4)^(4*(9/12))
A = 121(1 + 0.0375)^3
A = 121(1.0375)^3
A = 121(1.1147)
A = $134.83
So after 21 months, if Customer 1 moves his balance to Clearwater Credit Union, he will have approximately $134.83 in the Clearwater State Bank account.
Customer 1 deposits $100 in Clearwater State Bank account. The interest rate for the first year is 20% compounded semi-annually.
Amount after one year:
The interest will compound semi-annually, which means it will be applied twice in a year. The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $100
r = 20% = 0.2
n = 2 (compounded semi-annually)
t = 1 year
Plugging in these values into the formula, we get:
A = 100(1 + 0.2/2)^(2*1)
A = 100(1 + 0.1)^2
A = 100(1.1)^2
A = 100(1.21)
A = $121
So after one year, Customer 1 will have $121 in the Clearwater State Bank account.
Amount after 21 months:
After one year, Customer 1 decides to move his balance to Clearwater Credit Union. He will have $121 at this point. Clearwater Credit Union offers an interest rate of 15% compounded quarterly for the first year.
To calculate the amount after 21 months, we need to calculate the interest for the remaining 9 months (21 - 12 months).
Amount after 9 months:
The interest will compound quarterly, which means it will be applied four times in a year. The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
In this case:
P = $121
r = 15% = 0.15
n = 4 (compounded quarterly)
t = 9/12 year (9 months)
Plugging in these values into the formula, we get:
A = 121(1 + 0.15/4)^(4*(9/12))
A = 121(1 + 0.0375)^3
A = 121(1.0375)^3
A = 121(1.1147)
A = $134.83
So after 21 months, if Customer 1 moves his balance to Clearwater Credit Union, he will have approximately $134.83 in the Clearwater State Bank account.
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Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q.From the choices below, identify the amount Customer 1 will have in Clearwater State Bank after one year, and the amount Customer 1 will have after 21 months if he moves his balance at the end of the first year to Clearwater Credit Union. Make two selections.a)121b)135c)168d)186e)220Correct answer is option 'A,B'. Can you explain this answer?
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Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q.From the choices below, identify the amount Customer 1 will have in Clearwater State Bank after one year, and the amount Customer 1 will have after 21 months if he moves his balance at the end of the first year to Clearwater Credit Union. Make two selections.a)121b)135c)168d)186e)220Correct answer is option 'A,B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q.From the choices below, identify the amount Customer 1 will have in Clearwater State Bank after one year, and the amount Customer 1 will have after 21 months if he moves his balance at the end of the first year to Clearwater Credit Union. Make two selections.a)121b)135c)168d)186e)220Correct answer is option 'A,B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q.From the choices below, identify the amount Customer 1 will have in Clearwater State Bank after one year, and the amount Customer 1 will have after 21 months if he moves his balance at the end of the first year to Clearwater Credit Union. Make two selections.a)121b)135c)168d)186e)220Correct answer is option 'A,B'. Can you explain this answer?.
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