Question

1.   Suppose that a financial contract promised to pay $3,500 at the end of each year for five (5) years. The appropriate discount rate is 8%,    

Calculate the most you should pay for this ordinary annuity?

B.If you receive the same amount at the beginning of each year for five (5) years and the discount rate is the same, calculate the most you should pay?

Calculate the Effective Annual Rate (EAR) of a car loan which charges 7.5% interest per annum compounding on a weekly basis for five (5) years.

Answer 1

A. At the end of each year.

Formula: The present value of an ordinary annuity (PV)

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at Present)
C= Periodic cash flow. 3500
r =effective interest rate for the period. 0.08
n = number of periods. 5

PV = 3500× [1-(1+0.08)^-5]/0.08

PV = $13,974.48

Most you should pay $13,974.48

B. At the beginning of each year.

Formula: The present value of an annuity due (PV)

PV = {C× [1-(1+r)^-n]/r}×(1+r)}

PV = Present value (The cumulative amount available at Present).
C= Periodic cash flow.
r =effective interest rate for the period.
n = number of periods.

PV = {3500× [1-(1+0.08)^-5]/0.08}×(1+0.08)}

PV = $15,092.44

Most you should pay $15,092.44

C. Given interested rate which is compounded weekly is (R) 7.5%

Number of weeks in a year (m) = 52

Effective annual rate is = {[1+(R/m)]^m}-1

{[1+(0.075/52)]^52}-1
= 7.783%