Question

your claim has been settled and you will be receiving ten semi-annual payments of $8,000. The first payment will be received 9.5 years from now. if the discount rate is 14% per year compounded monthly, what is the present value of this settlement? (using casio fx-9750GII)

Answer 1

discount rate = 14% per year compounded monthly

effective discoun rate ( annual ) ,R= ( 1+ (stated interest rate/m))^m -1 ( where m = no. of months in a year)

= (1+(0.14/12))¹² -1 = (1.01166)¹² - 1 = 1.14925 - 1 = 0.14925 = 14.925%

semi-annual payment = $8000

no. of semi annual payments = 10

first payment is starting after 9.5 years

firstly we will calculate the present value of the 10 semi annual payments at the end of 9 years

PV₉ = A*((1+R)ⁿ - 1)/((1+R)ⁿ*R)

= 8000/((1+R)^0.5) + 8000/((1+R)¹​) + 8000/((1+R)^1.5​) + 8000/((1+R)²​) + 8000/((1+R)^2.5​) + 8000/((1+R)³​) + 8000/((1+R)^3.5​) + 8000/((1+R)⁴​) + 8000/((1+R)^4.5​) + 8000/((1+R)⁵​)

putting R = 14.925%

= 8000/((1+0.14925)^0.5) + 8000/((1+0.14925)¹​) + 8000/((1+0.14925)^1.5​) + 8000/((1+0.14925)²​) + 8000/((1+0.14925)^2.5​) + 8000/((1+0.14925)³​) + 8000/((1+0.14925)^3.5​) + 8000/((1+0.14925)⁴​) + 8000/((1+0.14925)^4.5​) + 8000/((1+0.14925)⁵​)

= 7462.472278 + 6961.061562 + 6493.341116 + 6057.047259 + 5650.068406 + 5270.434856 + 4916.309251 + 4585.977687 + 4277.841419 + 3990.409125

= $55664.96296

This is the present value of the payments at the end of 9 years

Now to calculate the present value at the end of year 0

PV₀ = PV₉ / ((1+R)⁹) =  $55664.96296/((1.14925)⁹) = 55664.96296/3.497281671 = $15916.63703

This is the required present value of payments today

I calculated the values using excel ( I do not posess the casio fx-9750GII )