💡 Solutions to homework

Week 1

Problem 1

To compare the two funds, we assume that equal investments of \(X\) are made at time 0.

John’s accumulation function is \[t^2+2t+1\]

Edna’s accumulation function is \[2t^{2}+1\]

To determine when Edna’s investment exceeds John’s, we set:

\[ X(2t^{2}+1)>X(t^{2}+2t+1)\]

which reduces to:

\[t^{2}-2t>0\] or \[t(t-2)>0\]

Thus, Edna’s fund exceeds John’s after 2 years.

Problem 2

\[PV=1000v+2000v^{3}=2540.15 \]

since \[v=1.075^{-1}\]

Problem 3

Discounting at \(10\%\), the net present values are \(4.59\),\(-2.36\) and \(-9.54\) for Projects A,B,and C respectively.

Take Project A as an example:

\[NPV=-800+500v+500v^{2}-175v^{3}+100v^{4}=4.59\]

since \[v=1.10^{-1}\]

Hence, only Project A should be funded.