Solve for the unknown interest rate in each of the following (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future Value $ 280 5 % $ 372 400 19 1,370 43,000 20 238,809 42,261 30 1,107,073 Explanation: 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 = $372 = $280(1 + r)5; r = ($372 / $280)1/5 – 1 = 0.0585, or 5.85% FV = $1,370 = $400(1 + r)19; r = ($1,370 / $400)1/19 – 1 = 0.0669, or 6.69% FV = $238,809 = $43,000(1 + r)20; r = ($238,809 / $43,000)1/20 – 1 = 0.0895, or 8.95% FV = $1,107,073 = $42,261(1 + r)30; r = ($1,107,073 / $42,261)1/30 – 1 = 0.1150, or 11.50% Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 5 $280 ±$372 N I/Y PV PMT FV Solve for 5.85% Enter 19 $400 ±$1,370 N I/Y PV PMT FV Solve for 6.69% Enter 20 $43,000 ±$238,809 N I/Y PV PMT FV Solve for 8.95% Enter 30 $42,261 ±$1,107,073 N I/Y PV PMT FV Solve for 11.50%

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

 

Present Value				Years		Interest Rate		Future Value
	$	280		5		%		$	372
		400		19					1,370
		43,000		20					238,809
		42,261		30					1,107,073

Explanation:

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 = $372 = $280(1 + r)5;		r = ($372 / $280)1/5 – 1	=	0.0585, or 5.85%
FV = $1,370 = $400(1 + r)19;		r = ($1,370 / $400)1/19 – 1	=	0.0669, or 6.69%
FV = $238,809 = $43,000(1 + r)20;		r = ($238,809 / $43,000)1/20 – 1	=	0.0895, or 8.95%
FV = $1,107,073 = $42,261(1 + r)30;		r = ($1,107,073 / $42,261)1/30 – 1	=	0.1150, or 11.50%

Calculator Solution:

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

Enter

5

$280

±$372

N

I/Y

PV

PMT

FV

Solve for

5.85%

Enter

19

$400

±$1,370

N

I/Y

PV

PMT

FV

Solve for

6.69%

Enter

20

$43,000

±$238,809

N

I/Y

PV

PMT

FV

Solve for

8.95%

Enter

30

$42,261

±$1,107,073

N

I/Y

PV

PMT

FV

Solve for

11.50%