Question

Solve for the unknown interest rate in each of the following: (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Present Value				Years			Interest Rate				Future Value
	$	805			4				%			$	1,561
		995			5								1,898
		24,000			16								150,832
		79,300			19								330,815

Answer 1

To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)^t

Solving for r, we get:

r = (FV / PV)^1/t – 1

FV = $1,561 = $805(1 + r)⁴

r = ($1,561 / $805)^1/4 – 1

r = 0.1801 or 18.01%

FV = $1,898 = $995(1 + r)⁵

r = ($1,898 / $995)^1/5 – 1

r = 0.1379 or 13.79%

FV = $150,832 = $24,000(1 + r)¹⁶

r = ($150,832 / $24,000)^1/16 – 1

r = 0.1217 or 12.17%

FV = $330,815 = $79,300(1 + r)¹⁹

r = ($330,815 / $79,300)^1/19 – 1

r = 0.0781 or 7.81%