Question

What is the relationship between the interest rate and future value? What is the relationship between the interest rate and present value? You can use intuition, math, or both to explain.

Answer 1

Future value = present value * (1 + interest rate)^{number of years}

Conversely, present value = future value / (1 + interest rate)^{number of years}

From these formulae, it can be concluded that :

• Higher the interest rate, higher the future value
• Higher the interest rate, lower the present value
• Lower the interest rate, lower the future value
• Lower the interest rate, higher the present value

Intuitively, this is because money has time value. That is, money received earlier is worth more than money received later. This is because money received earlier can be invested to earn a return. This is the opportunity cost of receiving money later. Therefore, higher this "opportunity cost'" (interest rate), lower the present value/higher the future value.