Question

Solve for the unknown interest rate in each of the following:

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

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For each of the following, compute the future value: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
  

Present Value				Years			Interest Rate				Future Value
	$	2,650			6			20	%			$
		9,453			19			8
		99,305			13			13
		237,382			29			3

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Answer 1

Part 1: Calculation of interest rates.

We need to calculate the interest rates for different given values.
Present value=$805
Years=4
Future value=$1561
Now, Future value=Present value*(1+interest rate)^(Number of years)
1561=805*(1+Interest rate)^4
=>1561/805=(1+Interest rate)^4
=>(1561/805)^(1/4)=1+Interest rate
=>(1.939130435)^(1/4)-1=Interest rate
=>1.180053659-1=Interest rate
=>0.180053659=Interest rate
=>Interest rate=0.180053659 or 18.01% (Rounded to two decimal places)

Present value=$995
Years=5
Future value=$1898
Future value=Present value*(1+interest rate)^(Number of years)
=>1898=995*(1+interest rate)^5
=>1898/995=(1+interest rate)^5
=>(1.907537688)^(1/5)=1+interest rate
=>1.137875183-1=Interest rate
=>0.137875183=Interest rate
=>Interest rate=0.137875183 or 13.79% (Rounded to two decimal places)

Present value=$24000
Years=16
Future value=$150832
Future value=Present value*(1+interest rate)^(Number of years)
=>24000=150832*(1+interest rate)^16
=>24000/150832=(1+interest rate)^16
=>(0.159117429)^(1/16)=1+interest rate
=>0.891471287-1=Interest rate
=>-0.108528713=Interest rate
=>Interest rate=-0.108528713 or -10.85% (Rounded to two decimal places)

Present value=$79300
Years=19
Future value=$330815
Future value=Present value*(1+interest rate)^(Number of years)
=>330815=79300*(1+interest rate)^19
=>330815/79300=(1+interest rate)^19
=>(4.171689786)^(1/19)=(1+interest rate)
=>1.07807258=1+interest rate
=>1.07807258-1=Interest rate
=>0.07807258=Interest rate
=>Interest rate=0.07807258 or 7.81% (Rounded up to two decimal places)

Part 2: Calculation of future values.
Present value=$2650
Years: 6
Interest rate=20%
Future value=Present value*(1+interest rate)^(Number of years)
=>Future value=2650*(1+20%)^(6)
=>Future value=2650*(1.2)^(6)
=>Future value=$7912.8576

Present value=$9453
Years: 19
Interest rate=8%
Future value=Present value*(1+interest rate)^(Number of years)
=>Future value=9453*(1+8%)^19
=>Future value=9453*(1.08)^19
=>Future value=$40796.32211

Present value=$99305
Years: 13
Interest rate=13%
Future value=Present value*(1+interest rate)^(Number of years)
=>Future value=99305*(1+13%)^13
=>Future value=99305*(1.13)^13
=>Future value=$486396.9926

Present value=$237382
Years: 29
Interest rate=3%
Future value=Present value*(1+interest rate)^(Number of years)
=>Future value=237382*(1+3%)^29
=>Future value=237382*(1.03)^29
=>Future value=$559406.2329