This assignment is on time value of money. when you answer the problems, write down the formula, plug the numbers and give me the answers. $1.$ You want to buy a house that costs $$209,215.$ The bank requires that you have a $10\%$ down payment. You have $$13,193$ today. If you put that money in a bank that offers $8\mathrm{.}4\%$ annual interest today, how many years before you have the down payment?

$2.$ You are going to save $$243$ at the end of each of the next $7$ years in a bank account with a $10\%$ interest rate. If you leave the money in the bank, how much will you have $3$ years after the date of the last payment?

$3.$ You put $$1,000$ into a bank account today and then add $$100$ at the end of each of the next $5$ years, with a $7\%$ interest rate, how much will you have on the date of the last payment?

$4.$ An investment promises $5$ equal annual payments of $$896,$ with the first payment occurring in $5$ years. If the interest rate is $6\%,$ what is the PV of the payments today $($i$.$e$.,$ at t$=0)?$

$5.$ What is the PV today of a $9$ payment annuity if the first payment of $$1,034$ occurs one year from today and the payments grow at $5\%$ annually? The interest rate is $10\%.$

$6.$ You need $$42,341$ to purchase your dream car, but only have $$20,811$ today. If you want to be able to purchase the car in $7$ years, what will the annual interest rate have to be$?$

$7.$ If a local lender charges interest of $2\mathrm{.}7\%$ per quarter, what is the effective annual rate $($EAR$)?$

$8.$ You are purchasing a house and will get a mortgage loan of $$605,116.$ The mortgage loan will be fully amortizing over $18$ years, with monthly payments and an annual interest rate of $10\%.$ What is the monthly payment?

$9.$ What is the PV of $$1,859$ received at the end of each of the next $8$ years? The discount rate is $5\mathrm{.}1\%.$

$10.$ SR Inc. has bonds with semi$-$annual payments. The bonds have $8$ years to maturity and are currently priced at $$990.$ At this price, the yield to maturity on the bonds is $9\mathrm{.}2\%.$ The par value of the bonds is $$1,000.$ What is the amount of each semi$-$annual coupon payment?