Question

Tara's lawyer gave her the following two options to settle her invoice:
(a) $2,000.00 in 1 month and the balance of $2,100.00 in 3 months.
(b) Two equal payments, one in 37 days and the other in 5 months.
If money earned 2.50% p.a., what was the value of the equal payments in Option (b) such that it is equivalent to the payments in Option (a)? Use now as the focal date for this question.
Round to the nearest cent

Answer 1

We will take now as focal date

First we will find the Present value of payments under option (a)

Interest rate = r = 2.50% p. a

Present value of payments under option (a) = Payment in 1 month / (1+ r)^{Time to payment} + Payment in 3 month / (1+ r)^{Time to payment} = 2000 / (1+ 2.50%)^1/12 + 2100 / (1+ 2.50%)^3/12 = 2000 / (1.0250)^1/12 + 2100 / (1.0250)^3/12 = 2000 / 1.00205983 + 2100 / 1.00619224 = 1995.8888 + 2087.0763 = 4082.9651

Let A = Equal payment under option (b)

If Two options are equivalent

Present value of payments under option (a) = present value of Payment under option (b) = 4082.9651

A / (1+2.5%)^37/365 + A / (1+2.5%)^5/12 = 4082.9651

A / (1.025)^37/365 + A / (1.025)^5/12 = 4082.9651

A / 1.002506222 + A / 1.010341698 = 4082.9651

0.99750004A + 0.989764A = 4082.9651

1.987264A = 4082.9651

A = 4082.9651 / 1.987264 = 2054.5660 = 2054.57 ( Rounded to nearest cent)

Value of equal payments in option (b) = 2054.57