Which sequence do I use to get the answer to this problem? Arithmetic or geometric? The answer is $36,000 but I do not no how to write it out or which one to use, Can someone please help me? Thank you.
A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?
how much is 21 tens
2.1
To solve this problem, you will need to use the concept of compound interest. Compound interest is when the interest accrued on an investment is added back to the principal amount, and then interest is calculated on the new total in subsequent periods.
In this particular problem, since the interest is compounded yearly, we can use an arithmetic sequence to calculate the total amount in the savings account after 10 years.
To calculate the total amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after compound interest
P = the principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the initial deposit (P) is $500, the annual interest rate (r) is 5% (or 0.05 as a decimal), the number of times interest is compounded per year (n) is 1 (since it is compounded yearly), and the number of years (t) is 10.
Plugging these values into the formula, we get:
A = 500(1 + 0.05/1)^(1*10)
A = 500(1 + 0.05)^10
A = 500(1.05)^10
A ≈ $814.45
So, after 10 years, there will be approximately $814.45 in the savings account.
Therefore, since the answer given ($36,000) is not consistent with the explained problem, it seems that there might be an error or misunderstanding with the information provided. Please double-check the problem statement or provide any additional context if you need further assistance.