Case Study F: TO BORROW FOR THE RRSP OR NOT TO BORROW? $$ The situation $$ Alex is debating whether to: a$)$ borrow $$15,000$ to invest into her RRSP at the beginning of the year and then pay off the loan in $4$ quarter$-$end payments starting as soon as they take out the loan OR b$)$ not borrow the money and instead contribute the same amount as the loan payment to her RRSP in quarter$-$end payments over the year. The data $$ The RRSP has an interest rate of $4\mathrm{.}1\%$ compounding monthly. $$ They tun $32$ years old on January $1$st and that is when they would either contribute to the RRSP in one lump sum or start quarterly contributions. $$ The loan has a rate of $4\mathrm{.}5\%$ compounded quarterly. $$ Your task $1.$ Calculate the value of their RRSP at retirement if they borrow the money to invest and makes no further contributions to their RRSP$.2.$ Calculate the final value gained by borrowing to invest by determining the interest gained less the cost in interest to borrow $$15,000$ for a year. $3.$ Calculate the RRSP value if instead the loan payment was contributed to their RRSP and no other contributions were made. $4.$ Determine which method was most beneficial to Alex and explain your reasoning. $$