Homework #$2$ TVM Problems

$1-$Suppose you will deposit the following amounts into your savings account, earning $7\%$ annually compounded interest. How much you will have at the end of the $4^{th}$ year?

$Yr1=$$$1,000$

$Yr2=$$$2,000$

$Yr3=$$$3,000$

$Yr4=$$$4,000$

$2-$ If you buy a factory for $$250,000$ and the terms are $20$ percent down, the balance to be paid off over $30$ years at a $12$ percent rate of interest on the unpaid balance, what are the $30$ equal annual payments?

$3-$You deposit $$5000$ today in an account earing $4\%$ annual interest and keep it for $5$ years. In $5$ years, you add $$15,000$ to your account, but the rate on your account changes to $8\%$ annual interest $($for existing balance and new deposit$).$ You leave the account untouched for an additional $10$ years. How much do you accumulate?

$4-$Two brothers each open IRAs in $2009$ and plan to invest $$3,000$ per year for the next $30$ years. John makes his first deposit on January $1,2009,$ and will make all future deposits on the first day of the year. Bill makes his first deposit on December $31,2009,$ and will continue to make his annual deposits on the last day of each year. At the end of $30$ years, How much the difference in the value of the IRAs $($rounded to the nearest dollar$),$ assuming an interest rate of $7\%$ per year, will be$?$

$5-$Bill borrowed $$100,000$ today that he must repay in $15$ annual end$-$of$-$year installments of $$10,000.$ What annual interest rate is Bill paying on his loan?

$6-$A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an equal amount each year into an investment account that earns $7\mathrm{.}5\%$ interest per year, starting on his first birthday. How much would you need to invest each year $($rounded to the nearest dollar$)$ to accumulate a million for your child by the time he is $35$ years old?

$7-$You have contracted to buy a house for $$250,000,$ paying $$30,000$ down and taking out a fully amortizing loan for the balance, at a $5\mathrm{.}7\%$ annual rate for $30$ years. What will your monthly payment be if they make equal monthly installments over the next $30$ years $($to the nearest dollar$)?$

$8-$An investment is expected to yield $$300$ in three years, $$500$ in five years, and $$300$ in seven years. What is the present value of this investment if our opportunity rate is $5\%?$