Question

Luis's lawyer gave her the following two options to settle her invoice:

(a) $1,900.00 in 1 month and the balance of $2,800.00 in 5 months.

(b) Two equal payments, one in 21 days and the other in 10 months.

If money earned 5.30% 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.

Answer 1

Here the present value of both the equal payments have to be equal to the present value of payments made in a above

Given interest rate is 5.3%

Now we will calculate the interest rate for 1 month and 5 months

We will calculate the interest rate for 21 days and 10 months

Accordingly

For 1 month Inteerst rate is 5.3 * 1/12 = 0.441667%

For 5 months the interest rate is 5.3 * 5/12 = 2.208333%

For 21 days the interest rate is 5.3 * 21/365 = 0.304932% ( We have taken 365 days a year)

For 10 months the interest rate is 5.3 * 10/12 = 4.416667%

Now we will discount the cash flows in a above

= 1900/1.004417 + 2800/1.022083

= 4631.147883

Now let us assume that the equal payments be X

Now X/1.003049 + X/1.044167

= X ( 0.99696 + 0.957702)

1.954661 X

Hence 1.954661 X = 4631.147883

X = 2369.284

Hence the equalised payments are $2369.284