If a security pays $55 in one year and $133 in three years, its present value is $150 if the interest rate is

10%

Step-by-step explanation:

What we will do is apply the present value formula that would be as follows:

PV = P1 / (1 + R) + P2 / (1 + R) ^ 2 + ... + Pn / (1 + R) ^ n

Where VP is the present value, P would be the payment in each corresponding year and R what we are looking for, the interest rate.

Replacing we have the following values:

150 = 55 / (1 + R) + 133 / (1 + R) ³

We have a cubic equation that here is very complex to answer so we are going to use the symbolab tool.

Next we can see how it calculates the value of R step by step.

https://es.symbolab.com/solver/step-by-step/150%20%3D%2055%20%2F%20%5Cleft(1%20%2B%20R%5Cright)%20%2B%20133%20%2F%20%5Cleft(1%20%2B%20R%5Cright)%20%C2%B3

The result is that R equals approximately 0.09976, therefore the interest rate is 9.976%, or rounding 10%