suppose you put money into teo different bank accounts. In account #1 you deposit $500 and you will be earning 6% interest compounded quarterly. in account #2 you deposit $600 and you will be earning 5% interest compounded annually. Which statement below best describes the relationship between the amount if money in account #1 and account #2 after 10 years have passed. Assume that during these years you will not withdraw any money
PLEASE HELP I DON'T UNDERSTAND
A:) Account #1 will have approximately $397 less than Account #2.
B:) Account #1 will have approximately $82 more than Account #2.
C:) Account #1 will have approximately $70 less than Account #2.
D:) Account #1 and Account #2 will have approximately the same amount of money in them.
Assuming you have the same choices as me, the answer is:
C:) Account #1 will have approximately $70 less than Account #2.
I got it right.
Murkle is right, the answer is C.
Well, let's clown around with this financial situation! Here's how I can help you understand the relationship between the two accounts.
After 10 years, Account #1 can be calculated using the formula for compound interest, which is A = P(1 + r/n)^(nt). In this case, P (the principal) is $500, r (the interest rate) is 6% or 0.06, n (the number of times interest is compounded per year) is 4 (quarterly), and t (the number of years) is 10. So, Account #1 would be worth $500(1 + 0.06/4)^(4*10).
For Account #2, since the interest is compounded annually, you can calculate it with the same formula, but with a different interest rate and compounding frequency. In this case, P is $600, r is 5% or 0.05, n is 1 (annual), and t is 10. So, Account #2 would be worth $600(1 + 0.05/1)^(1*10).
Now, to understand the relationship between the two amounts, you can compare the values of Account #1 and Account #2 after 10 years. If Account #1 is greater than Account #2, you can say the money in Account #1 has surpassed Account #2, and vice versa.
But wait! Before we continue, let me tell you a joke to keep the numbers from overwhelming you:
Why did the bank go to the comedy club?
To improve their "interest" rates!
Alright, back to business. Calculate the values of Account #1 and Account #2 after 10 years using the formulas above, and compare the results. This will help you understand the relationship between the two amounts.
To understand the relationship between the amount of money in account #1 and account #2 after 10 years, we can calculate the future values of both accounts based on the given interest rates and compounding frequencies.
First, let's calculate the future value of account #1 (the account with $500 deposit and a 6% interest rate compounded quarterly) after 10 years. We can use the formula for compound interest:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)
In this case, the principal is $500, the interest rate is 6%, and it's compounded quarterly, so the number of compounding periods per year is 4. Plugging in the values, we have:
Future Value of account #1 = $500 * (1 + (0.06 / 4))^(4 * 10)
Calculating this, we find that the future value of account #1 after 10 years is approximately $895.42.
Next, let's calculate the future value of account #2 (the account with $600 deposit and a 5% interest rate compounded annually) after 10 years. Again, using the compound interest formula:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)
Here, the principal is $600, the interest rate is 5%, and it's compounded annually, so the number of compounding periods per year is 1. Plugging in the values, we have:
Future Value of account #2 = $600 * (1 + (0.05 / 1))^(1 * 10)
Calculating this, we find that the future value of account #2 after 10 years is approximately $930.07.
Now, we can compare the future values of both accounts. Account #2 has a higher future value ($930.07) compared to account #1 ($895.42) after 10 years. Therefore, we can conclude that the amount of money in account #2 is greater than the amount of money in account #1 after 10 years.
So, the statement that best describes the relationship between the amounts of money in account #1 and account #2 after 10 years is that the amount of money in account #2 is greater than the amount of money in account #1.
well, either
#1 < #2
or
#1 > #2