Benjamin had to make payments of $1,500.00 and $2,600.00 in 12 months and 14 months, respectively, to a raw material supplier. What single payment in 3 months would settle both these payments? Assume a simple interest rate of 7.90% p.a. and use 3 months from now as the focal date.
To find the single payment that would settle both these payments in 3 months, we can use the concept of present value. The present value is the current value of a future amount taking into account the interest rate and the time period.
First, let's calculate the present value of the first payment of $1,500.00 due in 12 months. We will use the formula for present value:
Present Value = Future Value / (1 + r)^n
Where:
Future Value = $1,500.00
r = annual interest rate = 7.90% = 0.079 (converted to decimal)
n = number of years = 12/12 = 1 (converted to years as the interest rate is annual)
Using these values in the formula, we have:
Present Value of first payment = $1,500.00 / (1 + 0.079)^1
Present Value of first payment = $1,500.00 / (1.079)
Present Value of first payment = $1,392.44
Next, let's calculate the present value of the second payment of $2,600.00 due in 14 months:
Present Value of second payment = $2,600.00 / (1 + 0.079)^(14/12)
Present Value of second payment = $2,600.00 / (1.079)^(1.167)
Present Value of second payment = $2,487.69
Now, let's add the present values of both payments to find the single payment that would settle both.
Total present value = Present Value of first payment + Present Value of second payment
Total present value = $1,392.44 + $2,487.69
Total present value = $3,880.13
Therefore, a single payment of $3,880.13 made in 3 months would settle both the payments.