Solve for the unknown interest rate in each of the following

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.):

 

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

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

  

0		5
–$210		$270

FV = $270 = $210(1 + r)⁵

r = ($270/$210)^1/5 – 1

r = .0515, or 5.15%

0		19
–$330		$997

FV = $997 = $330(1 + r)¹⁹

r = ($997/$330)^1/19 – 1

r = .0599, or 5.99%

0		20
–$36,000		$175,751

FV = $175,751 = $36,000(1 + r)²⁰

r = ($175,751/$36,000)^1/20 – 1

r = .0825, or 8.25%

0		30
–$35,261		$764,676

FV = $764,676 = $35,261(1 + r)³⁰

r = ($764,676/$35,261)^1/30 – 1

r = .1080, or 10.80%

Calculator Solution:

Enter

5

$210

±$270

N

I/Y

PV

PMT

FV

Solve for

5.15%

Enter

19

$330

±$997

N

I/Y

PV

PMT

FV

Solve for

5.99%

Enter

20

$36,000

±$175,751

N

I/Y

PV

PMT

FV

Solve for

8.25%

Enter

30

$35,261

±$764,676

N

I/Y

PV

PMT

FV

Solve for

10.80%