Question

Financial Management


FATIMA wants to borrow $50,000 for a period of 6 years.
The lenders offers her a choice of three payment structures:
1) Pay all of the interest (10 % per year) and principal in one lump sum at the end of 6 years;
2) Pay interest at the rate of 10 % per year for 5 years and then a final payment of interest and principal at the end of the 6th year;
3) Pay 6 equal payments at the end of each year inclusive of interest and part of the principal.

​Under which of the three options will FATIMA pay the least interest and why?
​Calculate the total amount of the payments and the amount of interest paid under each alternative.?

Answer 1

1) We are given the following information:

Value borrowed at time 0	PV	$          50,000.00
rate of interest	r	10.00%
number of years	n	6
Future value	FV	To be calculated

We need to solve the following equation to arrive at the required FV

So the FV is $88578.05

Interest is FV-PV = 88578.05 - 50000 =38578.05

2) In this case as interest is paid off each year, it is not accumulated so there is no interest on interest so calculations are done in the following manner:

As in the year 6 also the same interest is pai along with the principal repayment of 50000, so the total amount paid off was 50000+30000 = 80000

3)

We are given the following information:

Annual payment	PMT	To be calculated
rate of interest	r	10.00%
number of years	n	6
Present value	PV	$          50,000.00

We need to solve the following equation to arrive at the required PMT

Annual PMT is 11480.37 and the total amount paid off is 11480.37 x 6 =  $68,882.21

Total interest is 68882.21 - 50000 = 18882.21

So under option 3 Fatima pays the lowest interest