Deandre deposited $4000 into an account with 2.1% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 9 years?
Question
Deandre deposited $4000 into an account with 2.1% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 9 years?
Solution
To solve this problem, we will use the formula for compound interest, which is:
A = P (1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal form, so 2.1% becomes 0.021).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case:
- P = $4000
- r = 0.021
- n = 12 (since the interest is compounded monthly)
- t = 9
Substituting these values into the formula, we get:
A = 4000 * (1 + 0.021/12)^(12*9)
Now, we just need to calculate the value of A.
A = 4000 * (1 + 0.00175)^(108) A = 4000 * (1.00175)^(108) A = 4000 * 1.195618 A = $4782.47
So, Deandre will have approximately $4782.47 in the account after 9 years.
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