You want to receive $\mathrm{\$}600$ at the end of each year for 4 years. Interest is $5.1\mathrm{\%}$ 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 $\mathrm{\$}◻$.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
(b) The interest is $\mathrm{\$}$
(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 $\boxed{{\displaystyle 2122.64}}$

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 $\boxed{{\displaystyle 277.36}}$