$3\mathrm{.}4\mathrm{.}2$ A loan of $15,000$ is repaid by annual payments of principal starting one year after the loan is made, plus quarterly payments of interest on the outstanding balance at a quarterly rate of $4\%.$ Find the present value of the payments to yield an investor a quarterly rate of $3\%$ if the principal payments are

$244>$ CHAPTER $3$

$($a$)1000$ per year for $15$ years; or

$($b$)1000$ in the $1^{th}$ year, $2000$ in the $2^{nd}$ year,..., $5000$ in the $5^{th}$ year; or

$($c$)5000$ in the $1^{st}$ year, $4000$ in the $2^{nd}$ year,..., $1000$ in the $5^{th}$ year.