Question

You have to choose how to invest a sudden windfall, and the two investments between which

you are trying to decide have the following terms. Investment A will pay a monthly dividend of
$100 along with 0.1% of the principal (the principal is the amount invested). The other pays a
straight 0.2% of the principal.
Which of these is likely to be best for small amounts of principal?
Which is likely to be best for large amounts? Explain.
Find the boundary - the amount at which the two pay the same.

Answer 1

Investment A pays a monthly dividend of $100 plus 0.1% of the principal, while Investment B pays 0.2% of the principal. For small amounts of principal, Investment A may be better due to the significant monthly dividend of $100. However, for larger amounts of principal, Investment B could yield higher returns.

Step-by-step explanation:

Investment A

• Monthly dividend: $100 + 0.1% of the principal

Investment B

• 0.2% of the principal

To determine which investment is best for small amounts of principal, compare the monthly dividends. If the principal is small, the monthly dividend of $100 from Investment A could be more significant compared to the 0.2% of the principal from Investment B. However, for larger amounts of principal, the 0.2% of the principal from Investment B could yield higher returns due to compounding interest.

To find the boundary where the two investments pay the same, set up an equation with P as the principal: 100 + 0.001P = 0.002P. Solve for P to find the amount at which the two investments pay the same.