# Interest Rate Risk

The value of fCash changes as interest rates change. This is called

**interest rate risk**.**As interest rates increase, the cash value of fCash decreases. As interest rates decrease, the cash value of fCash increases.**This means that you can make or lose money when you exit fCash before maturity in addition to the amount you earn from interest accrual.

For example, here is the value of 100 fCash with six months left to maturity at an interest rate of 5% vs. an interest rate of 8%.

// 100 fCash value with six months to maturity at 5% interest rate

cash = 100 / e^(0.05 * 0.5) = 97.53

// 100 fCash value with six months to maturity at 8% interest rate

cash = 100 / e^(0.08 * 0.5) = 96.08

Let's look at an example that includes transaction cost where a user lends 100 USDC at 5% for one year and then exits after six months when the interest rate has decreased to 3%.

// Lending 100 USDC at 5% for one year with 0.3% transaction fee

fCash = 100 * e^(.047 * 1) = 104.81 fCash

// Selling 104.81 fCash after six months with interest rate at 3% and 0.3% fee

cash = 104.81 / e^(.033 * 0.5) = 103.09

In this example, the user has earned 3.09 USDC in six months. This means that they have achieved an APY of ~6.18% even though they initially lent at a fixed rate of 5%! This extra earning on top of their interest accrual comes from the fact that fCash has appreciated in value due to the decrease in interest rates.

Longer-dated fCash is more sensitive to interest rate changes than shorter-dated fCash. This means that the greater the time to maturity, the more the cash value of fCash will change as interest rates change.

Let's look at an example of how much the value of fCash changes when it is has one year until maturity vs. three months to maturity.

// 100 one-year fCash value at interest rates of 5% and 8%

cash = 100 / e^(0.05 * 1) = 95.12

cash = 100 / e^(0.08 * 1) = 92.31

cash value change = 2.81

// 100 three-month fCash value at interest rates of 5% and 8%

cash = 100 / e^(0.05 * 0.25) = 98.76

cash = 100 / e^(0.08 * 0.25) = 98.02

cash value change = 0.74

In this example, the 1 year fCash changed in value ~4x more than the 3 month fCash for the same change in interest rates. Interest rate risk scales linearly with time to maturity. As fCash gets closer to maturity, the amount that its cash value will change due to a change in interest rates gets closer and closer to 0.