$7.$ Suppose you take out a $$10,000$ loan at a $6\%$ nominal annual rate. The terms of the loan require you to make $12$ equal end$-$of$-$month payments each year for $4$ years, and then an additional final $($balloon$)$ payment of $$4,000$ at the end of the last month. What will your equal monthly payments be$?8.$ A homeowner just obtained a $30-$year amortized mortgage loan for $$150,000$ at a nominal annual rate of $6\mathrm{.}5\%,$ with $360$ end$-$of$-$month payments. What percentage of the total payments made during the first $3$ months will go toward payment of interest?$9.$ a$)$ What would the future value of $$125$ be after $8$ years at $8\mathrm{.}5\%$ compound interest?b$)$ Suppose a Government of Canada bond promises to pay $$1,000$ five years from now. If the going interest rate on $5-$year government bonds is $5\mathrm{.}5\%,$ how much is the bond worth today?c$)$ Suppose the Government of Canada offers to sell you a bond for $$747\mathrm{.}25.$ No payments will be made until the bond matures $5$ years from now, at which time it will be redeemed for $$1,000.$ What interest rate would you earn if you bought this bond at the offer price?d$)$ How many years would it take $$50$ to triple if invested in a bank that pays $3\mathrm{.}8\%$ per year?e$)$ You want to buy a new sports car $3$ years from now, and you plan to save $$4,200$ per year, beginning $1$ year from today. You will deposit your savings in an account that pays $5\mathrm{.}2\%$ interest. How much will you have just after you make the third deposit, $3$ years from now?f$)$ What is the PV of an ordinary annuity with $10$ payments of $$2,700$ if the appropriate interest rate is $6\mathrm{.}5\%?10.$ a$)$ Suppose you inherited $$275,000$ and invested it at $8\mathrm{.}25\%$ per year. How much could you withdraw at the end of each of the next $20$ years?b$)$ Whats the present value of a perpetuity that pays $$250$ per year if the appropriate interest rate is $5\%?$c$)$ At a rate of $6\mathrm{.}25\%,$ what is the present value of the following cash flow stream: $$0$ at Time $0$; $$75$ at the end of Year $1$; $$225$ at the end of Year $2$; $$0$ at the end of Year $3$; and $$300$ at the end of Year $4?$d$)$ An investment costs $$1,000($CF at t $=0)$ and is expected to produce cash flows of $$75$ at the end of each of the next $5$ years, then an additional lump sum payment of $$1,000$ at the end of the $5$th year. What is the expected rate of return on this investment?e$)$ Whats the future value of $$1,500$ after $5$ years if the appropriate interest rate is $6\%,$ compounded semiannually?f$)$ Pace Co$.$ borrowed $$25,000$ at a rate of $7\mathrm{.}25\%,$ simple interest, with interest paid at the end of each month. The bank uses a $360-$day year. How much interest would Pace have to pay in a $30-$day month?g$)$ A business uses delivery trucks and is considering purchasing model A or model B$.$Model A costs $$55,000,$ costs $$3500$ a year to maintain and lasts $5$ years then is junked while model B costs $$35,000,$ costs $$1300$ a year and lasts only $3$ years. Calculate the equivalent annual annuity for each model and identify the best choice all else being equal? Use a cost of capital of $5\%$ per year.