$1)$ A $$12,000$ loan is repaid by semiannual payments of $$1500$ each. Interest on the loan is $10\%$ compounded semiannually. How long will it take to pay off the loan?A$)10$ yearsB$)21$ yearsC$)10\mathrm{.}4$ yearsD$)5$ yearsE$)5\mathrm{.}2$ years$2)$ As of your $54$th birthday, you have accumulated $$269,000$ in your RRSP$.$ What size of end$-$of$-$month payments in a twenty$-$five year annuity will these funds purchase at age sixty$-$five if you make no further contributions? Assume that his RRSP and the investment in the annuity will earn $4\mathrm{.}25\%$ compounded monthly.A$)$ $$2,383\mathrm{.}89$B$)$ $$2,323\mathrm{.}89$C$)$ $$2,233\mathrm{.}89$D$)$ $$2,423\mathrm{.}89$E$)$ $$2,123\mathrm{.}893)$ Today, Barry reached his $50$th birthday and he has $$70,000$ in his retirement fund. His goal is to have $$500,000$ on his $65$th birthday. He can expect his investments to earn $13\%$ compounded semiannually.How much will he have to invest at the end of every six months for the next $15$ years in order to reach his goal?A$)$ $$926\mathrm{.}14$B$)$ $$1,722\mathrm{.}84$C$)$ $$2,388\mathrm{.}89$D$)$ $$428\mathrm{.}30$E$)$ $$4,978\mathrm{.}304)$ Investments of $$200$ at the beginning of every month have accumulated to $$405,515$ after $30$ years.Expressed as a monthly compounded nominal annual rate, what return have these investments provided?A$)8\mathrm{.}041\%$B$)11\mathrm{.}673\%$C$)9\mathrm{.}450\%$ D$)8\mathrm{.}747\%$E$)7\mathrm{.}875\%$