A simple Taylor Rule guides monetary policy
Inflation + 2+0.5*(Inflation - 2)+0.5*(Output Gap)

Short-term interest rates are determined by the Federal Reserve through monetary policy.

The Federal Reserve sets the short-term borrowing rates between banks (called the federal funds rate). This rate helps determine the risk-free short-term borrowing rate. You will notice this rate closely mirrors the rate on saving accounts. Banks can choose to borrow through the federal funds market or customers.

Long-term interest rates typically follow short-term rates (but not always).

The 10-year treasury rate typically leads consumer rates (including mortgage, car loans, student loans).

Long-term rates typically carry a higher return (prices are sensitive to inflationary risks).

Long-term rates are influences by the business cycle, expected inflation, federal deficits, and monetary policy (since Great Recession).

The risk premium is one of the more important economic indicators. The risk premium is measured as the spread between Baa corporate bonds and 10-year U.S. Treasury.

The yield curve is another important economic indicator... the yield curve is a plot that shows the yield on U.S. Treasuries across different maturities...

See these links:
https://www.nytimes.com/interactive/2015/03/19/upshot/3d-yield-curve-economic-growth.html

www.treasury.gov%2Fresource-center%2Fdata-chart-center%2Finterest-rates%2Fpages%2Ftextview.aspx%3Fdata%3Dyield&usg=AOvVaw2KQeOoWrVp_QxoWxsvbTnQ

https://www.frbsf.org/economic-research/indicators-data/treasury-yield-premiums/

An easy way to look at the yield curve is by taking the difference in rates between the long end and short end of the yield curve.

Turns out interest rates help provide a lot of insight into market participants expectations over future economic variables (GDP and expected inflation). In fact, they serve as a direct measure of inflation. The federal government sells TIPS (treasury inflation protected securities) where the face value adjusts with inflation. The difference between TIPS and normal treasuries show future inflation.

Other factors that play a role in determining long-term interest rates

Government borrowing

Monetary policy
-Current balance sheet https://www.clevelandfed.org/our-research/indicators-and-data/credit-easing.aspx

Foreign capital inflows