Amri has two debts, RM5,000 due in two years and another RM3,000 due in four years. If Harold wishes to settle the two debts 3½ years from now, find this single payment if money is worth 8% compounded quarterly
To find the single payment to settle the two debts, we need to find the present value of each debt and then add them together.
For the first debt of RM5,000 due in two years, we can use the formula for present value:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = present value (what we want to find)
FV = future value (RM5,000)
r = interest rate per period (8% compounded quarterly, so 8%/4 = 2%)
n = number of compounding periods per year (quarterly, so 4)
t = number of years (2)
Plugging in the values:
PV1 = RM5,000 / (1 + 0.02/4)^(4*2)
PV1 = RM5,000 / (1 + 0.005)^(8)
PV1 = RM5,000 / (1.005)^8
PV1 = RM5,000 / 1.0406
PV1 ≈ RM4,797.73
For the second debt of RM3,000 due in four years, we can use the same formula:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = present value (what we want to find)
FV = future value (RM3,000)
r = interest rate per period (8% compounded quarterly, so 8%/4 = 2%)
n = number of compounding periods per year (quarterly, so 4)
t = number of years (4)
Plugging in the values:
PV2 = RM3,000 / (1 + 0.02/4)^(4*4)
PV2 = RM3,000 / (1 + 0.005)^(16)
PV2 = RM3,000 / (1.005)^16
PV2 = RM3,000 / 1.0849
PV2 ≈ RM2,760.94
Adding the present values of the two debts:
Total PV = PV1 + PV2
Total PV ≈ RM4,797.73 + RM2,760.94
Total PV ≈ RM7,558.67
Therefore, the single payment to settle the two debts 3½ years from now is approximately RM7,558.67.