Question

2. What is the present value of the following uneven cash flow stream? The appropriate interest rate is 5.6%, compounded annually. Note that the final cash flow represents a project where there may be reclamation or other “end of project” costs which are greater than any final income and/or salvage value.
   

3. What annual interest rate will cause $2,750 to grow to $4,200 in 5 years, assuming annual compounding? Show your answer to 2 decimals (x.xx%)

4. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually — holding the stated interest rate constant? Explain your answer.

5. a) What is the future value of $2,750 after six years under 5.6% semiannual compounding

9b) What is the effective annual rate for 5.6% interest with semiannual compounding? Be sure to show your EAR answer to 2 decimals, that is xx.xx%

9c) What is the future value of $2,750 after six years under 5.6% quarterly compounding?

9d) What is the effective annual rate (EAR) for 5.6% interest with quarterly compounding?

9e) Explain how the effective annual rate changes based on the number of compounding periods per year.

9f) What is the future value of $2,750 after six years under 5.6% daily compounding? Assume 365 day years and do not do any interim rounding.

9g) What is the effective annual rate for 5.6% (APR) interest with daily compounding?

6. Will the effective annual rate ever be equal to the simple (quoted) rate? Explain.

Answer 1

Q) What annual interest rate will cause $2,750 to grow to $4,200 in 5 years, assuming annual compounding

Ans: Formula for FV=PV(1+r)^t ; solving for r we get r=((FV/PV)^(1/t)-1) = ((4200/2750)^(1/5)-1) = 8.84%

a) Future value of 2750 after 6 yrs @5.6% semiannual compounding

=> FV = PV*(1+r)^t

Since it is compounded semi annually, t=6*2=12 & r=5.6%/2 = 2.8%(2 is for semi annual compounding)

= FV=2750*(1+2.8%)^12 = 3830.45

b) The formula for Effective annual Rate is ((1+i/(t))^t)-1; where t is the number of period, here its 2 since its semiannual compounding; EAR = ((1+5.6%/(2))^2)-1 = 5.68%

c) future value of $2,750 after six years under 5.6% quarterly compounding

=> FV = PV*(1+r)^t

Since it is compounded semi annually, t=6*4=24 & r=5.6%/4 = 1.4% (4 is for quarterly compounding)

= FV=2750*(1+1.4%)^24 = 3839.23

d) effective annual rate (EAR) for 5.6% interest with quarterly compounding

formula for Effective annual Rate is ((1+i/(t))^t)-1; where t is the number of period, here its 4 since its quarterlycompounding; EAR = ((1+5.6%/(4))^4)-1 = 5.72%