Question

Find the present value of $350 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

1. 6% nominal rate, semiannual compounding, discounted back 5 years.

   $   

2. 6% nominal rate, quarterly compounding, discounted back 5 years.

   $   

3. 6% nominal rate, monthly compounding, discounted back 1 year.

   $   

Answer 1

PV = FV [ 1/ (1+r)ⁿ ]

^where,

^{PV = Present Value}

^{r = semi annual interest rate}

^{n = number of periods}

^{a) FV = $ 350}

^{As it is compounded semi annually, compounding is done twice a year}

r = 6/2 = 3

n = 5years*2 = 10

Therefore,

PV = 350 [ 1/ (1+3%)¹⁰ ]

= $260.43

b) FV= $350

As it is compounded quarterly, compounding is done 4 times a year

r = 6/4 = 1.5%

n = 5years*4 = 20

PV = 350 [ 1/ (1+1.5%)²⁰ ]

= $259.86

c) FV= $350

As it is compounded monthly, compounding is done 12 times a year

r = 6/12 = 0.5%

n = 1year*12 = 12

PV = 350 [ 1/ (1+0.5%)¹² ]

= $329.67