Investing
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One of the two great forces that help keep the money supply balanced, investment can be described as a function of income and interest.
There are many other ways of describing investments as they bring about different connotations in economics and personal finance; diving deeper would mean discussing a topic just about as large as interest, if not larger. What we are interested in discovering here is how interest and interest rates affect what we can earn from investing.
Bonds
Bond prices move in the opposite direction to that of interest rates. They give back fixed earnings compared to other investments that are affected by the changes in interest rates. Longer bond maturities usually mean higher yields than shorter-term ones since they pose a higher risk over the time its price fluctuates, as well as the market interest rates.
The yield curve (also the term structure of interest rates) that graphs the market's perception of how future interest rates will turn out. Three typical types of yield curves are the normal yield curve, the flat yield curve, and the inverted yield curve. A more accurate curve, the spot-rate curve, takes into account the variations in coupon rates, since not all the time do people reinvest at the same rate.
Stocks
In stocks, call premiums typically rise when interest rates increase. The opposite happens with put premiums. Interest rates are not considered to be that influential on stock prices, but it is unwise to take them for granted.
Mutual Funds
Since mutual funds are only a collection of stocks and bonds, it may seem that such an investment is just an opportunity to try out more than one type of investment. Mutual funds are whole systems in themselves and it is important to inspect most specially the fees and costs involved.
As you have noticed, while there may be some relationship that can be drawn between gains from an investment vehicle and the trends of interest rates, other factors should also be considered, like taxes and inflation rates, leaving you with an overall, effective yield that is quite different from one considered with interest rates alone.
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