A debt of Rm7000 mature at the end of the second year and another RM8,000 at the end of six years. If the debtor wishes to pay his debts by making one payment at the end of the fifth year . Find the amount he must pay if money is worth 6% compounded semi annually using present as the focal date
To find the amount the debtor must pay at the end of the fifth year, we need to find the present value of the two debts and bring them back to the focal date.
For the debt of RM7000 maturing at the end of the second year, we need to bring it back to the focal date (present date). Using the compound interest formula:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value
FV = Future Value
r = interest rate
n = number of compounding periods per year
t = number of years
Plugging in the values:
PV1 = 7000 / (1 + 0.06/2)^(2*2)
= 7000 / (1 + 0.03)^4
= 7000 / (1.03)^4
≈ 6371.02
For the debt of RM8000 maturing at the end of the sixth year:
PV2 = 8000 / (1 + 0.06/2)^(2*6)
= 8000 / (1 + 0.03)^12
≈ 6143.11
Now, we need to bring both present values back to the focal date (end of the fifth year). We can discount each present value using the same compound interest formula:
DV = PV / (1 + r/n)^(n*t)
Where:
DV = Discounted Value (present value at a different focal date)
PV = Present Value
r = interest rate
n = number of compounding periods per year
t = number of years
For PV1:
DV1 = 6371.02 / (1 + 0.06/2)^(2*3)
= 6371.02 / (1 + 0.03)^6
≈ 5582.30
For PV2:
DV2 = 6143.11 / (1 + 0.06/2)^(2*1)
= 6143.11 / (1 + 0.03)^2
≈ 5957.23
Now, we can find the total amount the debtor must pay at the end of the fifth year by summing up the discounted values:
Total payment = DV1 + DV2
≈ 5582.30 + 5957.23
≈ 11539.53
Therefore, the debtor must pay approximately RM11,539.53 at the end of the fifth year.