Final answer:
To find the value of the deposit three years after the change in the interest rate, we can use compound interest formulas. Using the given initial deposit of $2000, 6% interest rate compounded monthly for four years, and 7% interest rate compounded quarterly for three years, we can calculate the final value of the deposit to be $2165.55.
Step-by-step explanation:
To calculate the value of the deposit three years after the change in the rate of interest, we need to first find the value of the deposit after four years using the 6% interest rate compounded monthly. We can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (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. Plugging in the given values, we get:
A = 2000(1 + 0.06/12)^(12 x 4) = $2125.55
Next, we need to find the value of the deposit after three years using the 7% interest rate compounded quarterly. Using the same formula, we get:
A = 2125.55(1 + 0.07/4)^(4 x 3) = $2165.55
Therefore, the value of the deposit three years after the change in the rate of interest is $2165.55.