$1$a$.$ What is the ending value $($future value$)$ of a one$-$year project that requires an initial investment of $$100$ and generates an interest rate of $15\%?$

$1$b$.$ What is the current value $($present value$)$ of a one$-$year investment that provides an interest rate of $10\%$ and has an expected future value of $$220?$

$1c.$ What is the ending value $($future value$)$ of a three$-$year project that requires an initial investment of $$100$ and generates an interest rate of $8\%?$

$1$d$.$ What is the ending value $($future value$)$ of a seven$-$year project that requires an initial investment of $$250$ and generates an interest rate of $11\%?$

$1$e$.$ What is the ending value $($future value$)$ of a twelve$-$year project that requires an initial investment of $$375$ and generates an interest rate of $5\%?$

$1$f$.$ What is the current value $($present value$)$ of a three$-$year investment that provides an interest rate of $10\%$ and has an expected future value of $$330?$

$1g.$ What is the current value $($present value$)$ of a seven$-$year investment that provides an interest rate of $12\mathrm{.}5\%$ and has $a11$ expected future value of $$1,234\mathrm{.}56?$

$1$h$.$ What is the current value $($present value$)$ of a seven$-$year investment that provides an interest rate of $12\mathrm{.}0\%$ and has an expected future value of $$1,234\mathrm{.}56?$

$1$i$.$ What is the current value $($present value$)$ of a seven$-$year investment that provides an interest rate of $11\mathrm{.}0\%$ and has an expected future value of $$1,234\mathrm{.}56?$

$1$j$.$ In questions $1g-1i,$ we looked for the present value of an investment. In each of these questions, the investment had the same terminal value $($future value $=$$$1,234\mathrm{.}56)$ and the same lifespan $(7$ years$).$ The only factor that changed is the interest rate. What happened to the current value $($present value$)$ of the investment as the interest rate changed? What does this tell you about the relationship between interest rates and present value?

As interest rate i fell from $12\mathrm{.}5\%$ to $12\mathrm{.}0\%,$ the present value increased from $$541\mathrm{.}3081$ to $$558\mathrm{.}4522.$ As interest rate i fell further, from $12\mathrm{.}0\%$ to $11\mathrm{.}0\%,$ present value increased more, from $$558\mathrm{.}4522$ to $$594\mathrm{.}6362.$

This suggests that there is an inverse $($opposite$)$ relationship between the interest rate and the present value of an investment, ceteris paribus $($all else held constant$).$