8. Find the present value of $575 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.
15% nominal rate, semiannual compounding, discounted back 5 years.
15% nominal rate, quarterly compounding, discounted back 5 years.
15% nominal rate, monthly compounding, discounted back 1 year.
Solution :-
If 15% nominal rate, semiannual compounding
then Effective Annual Rate = ( 1 + 0.15 / 2 )2 - 1 = 0.1556 = 15.56%
If 15% nominal rate, quarterly compounding
then Effective Annual Rate = ( 1 + 0.15 / 4 )4 - 1 = 0.15865 = 15.865%
If 15% nominal rate, monthly compounding
then Effective Annual Rate = ( 1 + 0.15 / 12 )12 - 1 = 0.160755 = 16.075%
Now Present Value in Case of Semiannual Compounding = $575 / ( 1 + 0.1556 )5
= $575 * 0.485
= $279.017
Now Present Value in Case of Quarterly Compounding = $575 / ( 1 + 0.15865 )5
= $575 * 0.4789
= $275.36
Now Present Value in case of monthly Compounding =
= $575 / ( 1 + 0.16075 )
= $575 * 0.8615
= $495.37
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