You want to receive $\$ 600$ at the end of each year for 4 years. Interest is $5.1 \%$ compounded annually.
(a) How much would you have to deposit at the beginning of the 4-year period?
(b) How much of what you receive will be interest?
(a) The deposit is $\$ \square$.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
(b) The interest is $\$$
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Given that the annuity payment (PMT) is $600, the interest rate per period (r) is 5.1% or 0.051, and the number of periods (n) is 4 years, we can use the formula for the present value of an annuity to find the amount to be deposited at the beginning of the 4-year period. The formula is: \(P = PMT \times \frac{1 - (1 + r)^{-n}}{r}\)

Step 2 ：Substituting the given values into the formula, we get: \(P = 600 \times \frac{1 - (1 + 0.051)^{-4}}{0.051}\)

Step 3 ：Calculating the above expression, we find that \(P = 2122.637434235277\)

Step 4 ：Rounding to the nearest cent, the amount to be deposited at the beginning of the 4-year period is \(\boxed{2122.64}\)

Step 5 ：To find the total interest received over the 4-year period, we first calculate the total amount received, which is \(PMT \times n = 600 \times 4 = 2400\)

Step 6 ：The interest is the total amount received minus the initial deposit, so \(interest = 2400 - 2122.637434235277 = 277.36256576472306\)

Step 7 ：Rounding to the nearest cent, the total interest received over the 4-year period is \(\boxed{277.36}\)