What is the discounted value of ?$790.00 paid at the end of every month for 4 years if interest is 4% per annum compounded semi-annually?

 

Discounted Value = $35,011.03(Rounded off to Two Decimals)

Step-by-step explanation

• Monthly Amount Paid = $790.00 at the end of every month 

• Time Period(n) = 4 years = 4*12 = 48 Months

• Interest Rate =4% per annum compounded semi-annually =4/2 = 2% Effective per Semi Annual Period

• Effective monthly Interest Rate(r) = ((1+ Effective semi Annual Rate)^{^1/6}) -1

= (1.02)^^1/6)-10

= 1.00330587878 -1

= 00330587878

= 0.330587878% effective per Monthly rate

Calculation of Discounted Value or Present Value:

= Monthly Installment * Present value annuity Factor ( r%, n Period)

= Monthly Installment * Present value annuity Factor (0.330587878%, 48 Months)

= Monthly Installment * PVAF (0.330587878%, 48 Months)

= 790 * 44.317764552995

= $35011.0339967 so, Discounted Value = $35,011.03(Rounded off to Two Decimals)