Final answer:
The accumulated value at the end of 10 years is $1407.41. The current value at the end of 3 years is $449.95.
Step-by-step explanation:
To calculate the accumulated value at the end of 10 years, we need to find the accumulated value for each interest rate period and then add them together. First, we calculate the accumulated value for the first 4 years at 4% interest rate. We use the formula A = P(1+r)^t, where A is the accumulated value, P is the principal (initial deposit), r is the interest rate, and t is the time in years. Plugging in the values, we get A = 400(1+0.04)^4 = 400(1.04)^4 = 400(1.1699) = 467.96. Next, we calculate the accumulated value for the next 3 years at 5% interest rate. Using the same formula, we get A = 400(1+0.05)^3 = 400(1.05)^3 = 400(1.157625) = 463.05. Finally, we calculate the accumulated value for the last 3 years at 6% interest rate. Again, using the formula, we get A = 400(1+0.06)^3 = 400(1.06)^3 = 400(1.191016) = 476.40. Adding up the accumulated values from each period, we get 467.96 + 463.05 + 476.40 = 1407.41. Therefore, the accumulated value at the end of 10 years is $1407.41.
To find the current value at the end of 3 years, we need to calculate the accumulated value for the first 3 years at 4% interest rate. Using the formula A = P(1+r)^t, we get A = 400(1+0.04)^3 = 400(1.04)^3 = 400(1.124864) = 449.95. Therefore, the current value at the end of 3 years is $449.95.