well, either
#1 < #2
or
#1 > #2
PLEASE HELP I DON'T UNDERSTAND
#1 < #2
or
#1 > #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.
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.
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.