Question

Merina is scheduled to make two loan payments to Bradford in the amount of $1,000 each, two months and nine months from now. Merina doesn't think she can make those payments and offers Bradford an alternative plan where she will pay $775 seven months from now and another payment seven months later. Bradford determines that 8.5% is a fair interest rate. What is the amount of the second payment?

Answer 1

Let us find the PV of the paymnets as on Today
Interest rate is 8.5% pa.
PV factor for two months =1/(1.085)^(2/12) =	0.98649
PV factor for nine months =1/(1.085)^(9/12) =	0.94064
Let us find the PV of two paymnets payable under
original plan

Payments	Amt	PV Factor	PV of payment
Payment in 2 months	1,000	0.98649	986.49
Payment in 9 months	1,000	0.94064	940.64
Total:			1927.13

So PV of Orginal Paymnets =$1,927.13

Let us find the PV for the proposed payments
PV factor for seven months =1/(1.085)^(7/12) =	0.95352
PV factor for 14 months =1/(1.085)^(14/12) =	0.90921
Assume the second paymnet in 14 months is A.
Let us find the PV of two paymnets payable under
new plan

Payments	Amt	PV Factor	PV of payment
Payment in 7 months	775	0.95352	738.978
Paymnet in 14 months	A.	0.90921	A*0.90921

As both the PVs need to be same :

So, 738.98+A*0.90921=1927.13

A=1306.80

So the second paymnet should be $1,306.80