Question

Describe how to find interest rates and time requirements for problems using present value and future value.

Answer 1

Given the Present value (PV) and Future value (FV) and either interest rate (r) or time requirement (n), we can find the other variable.

1. Let's say we are given PV, FV and r. We will find time requirement using the formula: FV = PV * (1 + r)^n

FV = PV * (1 + r)^n

(1 + r)^n = FV/PV

n * ln(1 + r) = ln(FV/PV)

n = ln(FV/PV)/ln(1 + r)

2. Now, let's say we are given PV, FV and n. We will find interest rate using the formula: FV = PV * (1 + r)^n

FV = PV * (1 + r)^n

(1 + r)^n = FV/PV

(1 + r) = (FV/PV)^(1/n)

1 + r = (FV/PV)^(1/n) - 1

r = (FV/PV)^(1/n) - 1