Problem $(10$ points$).$

The following situations require the use of time value of money analysis to answer.

$\backslash$table$[[,\backslash$table$[[$VARIOUS SITUATIONS REQUIRING THE USE OF$],[$TIME VALUE OF MONEY ANALYSIS$]]],[($a$),\backslash$table$[[$Rickman wishes to accumulate $$40,000$ in six years in order to have enough money to pay$],[$for his child's education. If he can earn an annual rate of $8\%$ on his money, compounded$],[$monthly$,$ how much would he have to deposit at the end of each month in order to$],[$accomplish this?$]]],[($b$)$

$\backslash$table$[[$Selleck is going to open a savings account. He wishes to accumulate $$25,000$ in the account$],[$in five years. If he can earn $10\%$ per year on the account, compounded quarterly, how much$],[$will he have to deposit today in order to accomplish this goal?$]],],[($c$),\backslash$table$[[$What is the present value of a payment of $$500$ received at the end of each period under the$],[$following situations.$]]],[(1)$

$\backslash$table$[[$The $$500$ is received each quarter. The interest rate is $6\%$ per year, compounded$],[$quarterly$,$ and the payments will be received each quarter for ten years.$]],],[(2)$

$\backslash$table$[[$The $$500$ is received semiannually. The interest rate is $5\%$ per year, compounded$],[$semiannually$,$ and the payments will be received for five years.$]],]]$

REQUIRED: Use present and future value techniques to answer the questions above. Round all calculations to the nearest whole dollar. Round all interest rates used to four decimal places, where necessary.