Question

Present Value for Various Compounding Periods

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. 9% nominal rate, semiannual compounding, discounted back 5 years.

   $  

2. 9% nominal rate, quarterly compounding, discounted back 5 years.

   $  

3. 9% nominal rate, monthly compounding, discounted back 1 year.

   $  

Answer 1

Here we will use the following formula:

PV = FV / (1 + r%)n

where, FV = Future value, PV = Present value, r = rate of interest , n= time period

(a) For semi annual compounding:

Rate of interest = 9%/ 2 = 4.5%, Time period = 5 * 2 = 10 semi annual periods

Now,putting the values in the above equation, we get,

PV = $575 / (1 + 4.5%)10

PV = $575 / (1 + 0.045)10

PV = $575 / (1.045)10

PV = $575 / 1.55296942173

PV = $370.26

So, required present value is $370.26.

(b) For quarterly compounding:

Rate of interest = 9%/ 4 = 2.25%, Time period = 5 * 4 = 20 quarters

Now,putting the values in the above equation, we get,

PV = $575 / (1 + 2.25%)20

PV = $575 / (1 + 0.0225)20

PV = $575 / (1.0225)20

PV = $575 / 1.56050920068

PV = $368.47

So, required present value is $368.47.

(c) For monthly compounding:

Rate of interest = 9%/ 12 = 0.75%, Time period = 1* 12= 12 months

Now,putting the values in the above equation, we get,

PV = $575 / (1 + 0.75%)12

PV = $575 / (1 + 0.0075)12

PV = $575 / (1.0075)12

PV = $575 / 1.093806897

PV = $525.69

So, required present value is $525.69.