Question

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.

1. 15% nominal rate, semiannual compounding, discounted back 5 years.

2. 15% nominal rate, quarterly compounding, discounted back 5 years.

3. 15% nominal rate, monthly compounding, discounted back 1 year.

Answer 1

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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