Answer to Question #153964 in Finance for Hamza SAlee

Question

Tariq wants to borrow Rs.50,000 for a period of 5 years. The lenders offer him a choice of three payment structures:

i. Pay all of the interest (10% per year) and principal in one lump sum at the end of 5 years;

ii. Pay interest at the rate of 10% per year for 4 years and then a final payment of interest and principal at the end of the 5^th year;

iii. Pay 5 equal payments at the end of each year inclusive of interest and part of the principal.

a) Under which of the three options will Tariq pay the least interest and why? 

b) Calculate the total amount of the payments and the amount of interest paid under each alternative. 

Answer 1

i. Borrowed value PV = 50000

Rate of interest r = 10 %

Number of years n = 5

Future value:

$FV = PV \times (1+r)^n \\ = 50000 \times (1+0.1)^5 \\ = 80525.5$

Interest is

$FV-PV = 80525.5 -50000 \\ = 30525.5$

ii. Annual interest $= 50000 \times 0.1 = 5000$

Total interest $= 5000 \times 5 = 25000$

As in the year 5 also the same interest is pai along with the principal repayment of 50000, so the total amount paid off was 50000+25000 = 75000

iii. Annual payment = PMT

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

$PV = PMT \times \frac{1 -(1+r)^{-n}}{r} \\ 50000 = PMT \times \frac{1 -(1+0.1)^{-5}}{0.1} \\ PMT = 13189.87$

Annual PMT is 13189.87 and the total amount paid off is $13189.87 \times 5 = 65949.37$

Total interest $= 65949.37 - 50000 = 15949.37$

Under option (iii) Tariq pays the lowest interest.