The Timeline

You have just taken out a five$-$year loan from a bank to buy an engagement ring. The ring costs $$6000.$ You plan to put down $$2000$ and borrow $$4000.$ You will need to make annual payments of $$1250$ at the end of each year. Show the timeline of the loan from your perspective. How would the timeline differ if you created it from the bank's perspective?

You currently have a four$-$year$-$old mortgage outstanding on your house. You make monthly payments of $$2000.$ You have just made a payment. The mortgage has $26$ years to go $($i$.$e$.,$ it had an original term of $30$ years$).$ Show the timeline from your perspective. How would the timeline differ if you created it from the bank's perspective?

The Three Rules of Time Travel

$3.$ Calculate the future value of $$4000$ in

a$.$ Three years at an interest rate of $6\%$ per year.

b$.$ Six years at an interest rate of $6\%$ per year.

c$.$ Three years at an interest rate of $12\%$ per year.

d$.$ Why is the amount of interest earned in part $($a$)$ less than half the amount of interest earned in part $($b$)?$

$4.$ What is the present value of $$13,000$ received

a$.$ Ten years from today when the interest rate is $4\%$ per year?

b$.$ Twenty years from today when the interest rate is $8\%$ per year?

c$.$ Five years from today when the interest rate is $2\%$ per year?

$5.$ Your brother has offered to give you either $$60,000$ today or $$100,000$ in $12$ years. If the interest rate is $6\%$ per year, which option is preferable?

$6.$ Consider the following alternatives:

i$.$ $$140$ received in one year

ii$.$ $$230$ received in five years

iii. $$320$ received in ten years

Problems

$167$

a$.$ Rank the alternatives from most valuable to least valuable if the interest rate is $8\%$ per year.

b$.$ What is your ranking if the interest rate is only $4\%$ per year?

c$.$ What is your ranking if the interest rate is $17\%$ per year?

$7.$ Suppose you invest $$800$ in an account paying $2\%$ interest per year.

a$.$ What is the balance in the account after three years? How much of this balance corresponds to "interest on interest"?

b$.$ What is the balance in the account after $25$ years? How much of this balance corresponds to interest on interest?

$8.$ Your daughter is currently twelve years old. You anticipate that she will be going to college in six years. You would like to have $$127,000$ in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of $5\%$ per year, how much money do you need to put into the account today to ensure that you will have $$127,000$ in six years?

$9.$ You are thinking of retiring. Your retirement plan will pay you either $$100,000$ immediately on retirement or $$140,000$ five years after the date of your retirement. Which alternative should you choose if the interest rate is

a$.0\%$ per year?

b$.8\%$ per year?

c$.20\%$ per year?

$10.$ Your grandfather put some money in an account for you on the day you were born. You are now $18$ years old and are allowed to withdraw the money for the first time. The account currently has $$4200$ in it and pays a $12\%$ interest rate.

a$.$ How much money would be in the account if you left the money there until your $25$ th birthday?

b$.$ What if you left the money in the account until your $65$th birthday?

c$.$ How much money did your grandfather originally put in the account?

Valuing a Stream of Cash Flows

$11.$ Suppose you receive $$100$ at the end of each year for the next three years.

a$.$ If the interest rate is $7\%,$ what is the present value of these cash flows?

b$.$ What is the future value in three years of the present value you computed in $($a$)?$

c$.$ Suppose you deposit the cash flows in a bank account that pays $7\%$ interest per year. What is the balance in the account at the end of each of the next three years $($after your deposit is made$)?$ How does the final bank balance compare with your answer in $($b$)?$

$12.$ You have just received a windfall from an investment you made in a friend's business.