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

Present Value Years Interest Rate Future Value
$785 4 % $1,521
975 5 1,858
22,000 16 148,832
77,300 19 326,815

Present Value     Years      Interest Rate     Future Value

$785                        4                17.98%             $1,521

$975                        5                13.76%             $1,858

$22,000                  16               12.69%            $148,832

$77,300                   19               7.88%              $326,815

Explanation:

Present value is the value of future cash flow in present time calculated by discounting the cash flows on a given rate. Present value is calculated due to the opportunity of investment available if cash flow receive today.

Working

Use following formula to calculate the interest rate

PV  = FV / ( 1 + r )^n

$785 = $1,521 / ( 1 + r )^4

( 1 + r )^4 = $1,521 / $ 785

( 1 + r )^4 = 1.9376

( ( 1 + r )^4 )^1/4 = ( 1.9376 )^1/4

1 + r = 1.1798

r = 1.1798 - 1 = 0.1798 = 17.98%

PV  = FV / ( 1 + r )^n

$975 = $1,858/ ( 1 + r )^5

( 1 + r )^5 = $1,858 / $ 975

( 1 + r )^5 = 1.906

( ( 1 + r )^5 )^1/5 = ( 1.906 )^1/5

1 + r = 1.1376

r = 1.1376 - 1 = 0.1376 = 13.76%

PV  = FV / ( 1 + r )^n

$22,000 = $148,832 / ( 1 + r )^16

( 1 + r )^16 = $148,832 / $ 22,000

( 1 + r )^16 = 6.7651

( ( 1 + r )^16 )^1/16 = ( 6.7651 )^1/16

1 + r = 1.1269

r = 1.1269 - 1 = 0.1269 = 12.69%

PV  = FV / ( 1 + r )^n

$77,300 = $326,815 / ( 1 + r )^19

( 1 + r )^19 = $326,815 / $ 77,300

( 1 + r )^19 = 4.2279

( ( 1 + r )^19 )^1/19 = ( 4.2279 )^1/19

1 + r = 1.0788

r = 1.0788 - 1 = 0.0788 = 7.88%

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