2) Eight months ago, Louise agreed to pay Thelma $750 and $950 six and twelve months, respectively, from the date of the agreement. With each payment Louise agreed to pay interest at the rate of 9.5% pa. from the date of the agreement.
Louise could not follow the agreement, nothing was paid. Now she whishes to settle her obligations with a single payment, four months from now. What payment should Thelma be willing to accept if money can earn 7.75% ?
Can u share the answer
To find the payment that Thelma should be willing to accept, we need to calculate the present value of the future payments using the given interest rate of 7.75%.
To do this, we can use the formula for the present value of a future annuity payment:
PV = C × [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value of the annuity
C = Cash flow per period ($750 initially, $950 after 6 months)
r = Interest rate per period (7.75% or 0.0775 as a decimal)
n = Number of periods (6 months for the first payment, 12 months for the second payment)
Let's calculate the present value for each payment:
First payment (6 months from now):
PV1 = $750 × [(1 - (1 + 0.0775)^(-6)) / 0.0775]
Second payment (12 months from now):
PV2 = $950 × [(1 - (1 + 0.0775)^(-12)) / 0.0775]
Now, we need to find the present value of each payment four months from now, since Louise wants to settle her obligations with a single payment at that time. To do this, we will discount each payment by four months using the interest rate of 7.75%.
First payment (discounted by four months):
PV1_discounted = PV1 / (1 + 0.0775)^(4/12)
Second payment (discounted by four months):
PV2_discounted = PV2 / (1 + 0.0775)^(4/12)
Finally, we can find the single payment Thelma should be willing to accept by summing up the present values of the discounted future payments:
Single payment = PV1_discounted + PV2_discounted
Calculating the values using a calculator or spreadsheet, we get the result for Thelma's payment that Louise should be willing to accept.