Question

Find the present value of $400 due in the future under each of these conditions:

1. 11% nominal rate, semiannual compounding, discounted back 10 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

2. 11% nominal rate, quarterly compounding, discounted back 10 years. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

3. 11% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent.
   $   

What is the present value of a $300 perpetuity if the interest rate is 8%? If interest rates doubled to 16%, what would its present value be? Round your answers to the nearest cent.

Present value at 8%: $  

Present value at 16%: $  

Answer 1

a) Future value (FV)= $ 400

Semiannual rate (r) = 11/2 = 5.5%

Time period (n)=10*2 = 20

Present value(PV)= FV/(1+r)^n

= 400/(1+0.055)^20

= $ 137.09

b)

Future value (FV)= $ 400

Semiannual rate (r) = 11/4 = 2.75%

Time period (n)=10*4 = 40

Present value(PV)= FV/(1+r)^n

= 400/(1+0.0275)^40

= $ 135.14

c)Future value (FV)= $ 400

Semiannual rate (r) = 11/12 =0.916667 %

Time period (n)=1*12 = 12

Present value(PV)= FV/(1+r)^n

= 400/(1+0.00916667 )^12

= $ 358.51

d)

PMT= $ 300

Present value at 8%: PMT / rate = 300/0.08 = $ 3750

Present value at 16%: PMT / rate = 300/0.16 = $ 1875