Question

Two receipts of $1,200 each are desired at the end of years 6 and 8. To make these receipts possible, three EOY payments $200, $300, and $400 amounts will be deposited in a bank at the end of years 2, 4, and 6. The bank’s interest rate (i) is 12% per year compounded semi-annually (every half year).

1. Generate the cash follow

2. Determine the future value of this cash flow at year 8.

Answer 1

As per the question the desired receipts in the year 6 and 8 is =$1200

The end of years deposits in bank in year 2=$200, in year 4=$300 and in year 6=$400

Interest rate given by bank = 12%=0.12 per year compounded semi-annually

Though the interest is compounded semi annually or in very six month then compounding period in a year n=2

Effective interest rate (r) = (1 + i/n)ⁿ-1

Effective interest rate (r) = (1 + 0.12/2)²-1=0.1236=12.36%

(1)Based on the information given in the question the below cashflow diagram in prepared, where the horizontal axis represents the end of years. Though deposit in bank is a cash outflow they are shown in down arrow and cash receipts are cash inflow they are shown in up arrow in respective years.

(2)Future value (FV) of the cashflow at year 8=?

FV=-200(F/P,12.36%,6)-300(F/P,12.36%,4)-400(F/P,12.36%,2)+1200(F/P,12.36%,2)+1200

Cash outflow are shown with negative sign and cash inflow are shown with positive sign

And to estimate future value of each cash F =P(F/P,i,N) = P(1+i)^N

FV=-200(1+0.1236)⁶-300(1+0.1236)⁴-400(1+0.1236)²+1200(1+0.1236)²+1200

FV= -200(2.012196)-300(1.593848)-400(1.262477)+1200(1.262477)+1200

FV= -402.4393-478.1544-509.9908+1514.9724+1200 =$1329.3879   or Approx $1329.39

Future value (FV) of the cashflow at year 8= $1329.39