Question

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

Present Value Years Interest Rate Future Value
$270 4 % $338
390 18 1,231
42,000 19 210,390
41,261 25 613,284

Answer 1

5.78%

6.59%

8.85%

11.40%

Step-by-step explanation:

The formula for determining future value (FV) given present value is(PV) :

FV = PV (1 +r)^n

r = interest rate

n = number of years

1. $338 = $270 x (1 + r)^4

( $338 /$270)^0.25 = 1 + r

1.0577 = 1 +r

r = 1.0577 - 1

r = 5.78%

2. 1231 = 390 (1 + r)^18

(1231 / 390)^0.055556 = 1 + r

1.065941 = 1 + r

r = 1.065941 - 1

r = 6.59%

3. 210390 = 42000 (1 +r)^19

(210390 / 42000)^0.052632 = (1 +r)

1.088505 = 1 + r

r = 8.85%

4. 613,284 = 41,261 (1 + r)^25

(613,284 / 41,261)^0.04 = (1 + r)

1.113999 = 1 + r

r = 11.40%