III. Future Value$/$Present Value

At $45$ years of age, Seth figured he wanted to work only $10$ more years. Being a full$-$

time landlord had a lot of advantages: cash flow, free time, being his own boss$-$but it

was time to start thinking towards retirement. The real estate investments that he had

made over the last $15$ years had paid off handsomely. After selling a duplex and a four$-$

unit and paying the associated taxes, Seth had $$350,000$ in the bank and was debt$-$

free. With only $10$ years before retirement, Seth wanted to make solid financial

decisions that would limit his risk exposure. Fortunately, he had located another

property that seemed to meet his needs$-$an older, but well maintained four$-$unit

apartment. The price tag was $$250,000,$ well within his range, and the apartment would

require no remodeling. Seth figured he could invest the other $$100,000,$ and between

the two hoped to have $$1$ million to retire on by age $55.$

$($a$)$ Seth read an article in the local newspaper stating the real estate in the area had

appreciated by $5\%$ per year over the last $30$ years. Assuming the article is

correct, what would the future value of the $$250,000$ apartment be in $10$ years?

$($b$)$ Seth's current bank offers a $1-$year certificate of deposit account paying $2\%$

compounded semiannually. A competitor bank is also offering $2\%,$ but

compounded daily. If Seth invests the $$100,000,$ how much more money will he

have in the second bank after one year, due to the daily compounding?

$($c$)$ A friend of Seth's who is a real estate developer needs to borrow $$80,000$ to

finish a development project. He is desperate for cash and offers Seth $18\%,$

compounded monthly, for $2\mathrm{.}5$ years. Find the future value of the loan using the

future value table. Does this loan meet Seth's goals of low risk? How could he

reduce the risk associated with this loan?

$($d$)$ After purchasing the apartment, Seth receives a street, sewer, and gutter

assessment for $$12,500$ due in $2$ years. How much would he have to invest

today in a CD paying $2\%,$ compounded semiannually, to fully pay the

assessment in $2$ years?