Question

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

Present Value				Years			Interest Rate				Future Value
	$	1,100						11	%			$	1,955
		2,791						9					4,550
		34,505						14					395,620
		34,200						21					223,916

Answer 1

Answer a.

Present Value = $1,100
Interest Rate = 11%
Future Value = $1,955

Let number of years be ‘n’

Present Value * (1 + Interest Rate)^Year = Future Value
$1,100 * 1.11^n = $1,955
1.11^n = 1.7773
n * ln(1.11) = ln(1.7773)
n = 5.51 years

So, number of years is 5.51 years

Answer b.

Present Value = $2,791
Interest Rate = 9%
Future Value = $4,550

Let number of years be ‘n’

Present Value * (1 + Interest Rate)^Year = Future Value
$2,791 * 1.09^n = $4,550
1.09^n = 1.6302
n * ln(1.09) = ln(1.6302)
n = 5.67 years

So, number of years is 5.67 years

Answer c.

Present Value = $34,505
Interest Rate = 14%
Future Value = $395,620

Let number of years be ‘n’

Present Value * (1 + Interest Rate)^Year = Future Value
$34,505 * 1.14^n = $395,620
1.14^n = 11.4656
n * ln(1.14) = ln(11.4656)
n = 18.62 years

So, number of years is 18.62 years

Answer d.

Present Value = $34,200
Interest Rate = 21%
Future Value = $223,916

Let number of years be ‘n’

Present Value * (1 + Interest Rate)^Year = Future Value
$34,200 * 1.21^n = $223,916
1.21^n = 6.5473
n * ln(1.21) = ln(6.5473)
n = 9.86 years

So, number of years is 9.86 years