Answer: $91017.17865 / 12 = $7585.5987
Explanation:
To solve this problem, we need to first determine the total interest that will be earned on the account over the 5-year period. We can do this by using the formula for compound interest, which is:
A = P (1 + r/n) ^ nt
where A is the total amount of money in the account after the interest has been compounded, P is the initial deposit, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years the money is deposited.
In this case, the initial deposit is $10,000, the interest rate is 2.05%, the number of times the interest is compounded per year is 12 (because the interest is compounded monthly), and the number of years the money is deposited is 5. Plugging these values into the formula, we get:
A = 10000 (1 + 0.0205 / 12) ^ (12 * 5)
A = 10000 (1.001708333) ^ 60
A = 10000 (1.101717865)
A = 101017.17865
Therefore, the total amount of money in the account after 5 years will be $101017.17865.
Since Monica wants to save up $10,000, we can subtract this amount from the total amount in the account to find out how much she needs to deposit each month in order to reach her goal:
101017.17865 - 10000 = 91017.17865
Therefore, Monica needs to deposit $91017.17865 each month in order to save up $10,000 in 5 years. This means that she will need to deposit $91017.17865 / 12 = $7585.5987 per month in order to reach her goal.