Question

For each of the following loan options (a & b) compute the following values:

- annual loan payment

- proportion of principle and interest in the first annual payment

- total interest paid over the entire time line of the loan

-total principal paid over the entire time line of the loan

a. You have decided to purchase a capital asset using an 850,000 at a rate of 8% for 25 years.

b. You have decided to purchase a capital asset for 850,000 at a rate of 7% for 15 years.

c. Which option would you take and why? Explain.

Answer 1

a)

Annual Payment = (r x P)/ [1- (1+r)^-n]

r = Interest rate = 8 %

P = Principal = $ 850,000    

n = No. of periods = 25 years

Annual Payment = (0.08 x $ 850,000)/ [(1 – (1 + 0.08)^-25]

                                = $ 68,000/ [(1 – (1.08)^-25]

                               = $ 68,000 / [(1 - 0.146018)

                               = $ 68,000 / 0.853982 = $ 79,626.96

First annual payment = $ 79,626.96

Interest amount in first annual payment = $ 850,000 x 0.08 = $ 68,000

Principal paid = $ 79,626.96 - $ 68,000 = $ 11,626.96

Proportion of principal and interest in first annual payment = $ 11,626.96: $ 68,000 = 1: 5.848475

Total payment including principal and interest = $ 79,626.96 x 25 = $ 1,990,674.05

Total interest paid = Total payment – Principal = $ 1,990,674.05 - $ 850,000 = $ 1,140,674.05

Total principal = $ 850,000

b)

For r = 7 %, n = 15 years

Annual Payment = (0.07 x $ 850,000)/ [(1 – (1 + 0.07)^-15]

                                = $ 59,500/ [(1 – (1.07)^-15]

                               = $ 59,500/ [(1 - 0.362446)

                               = $ 59,500/ 0.637554 = $ 93,325.43

First annual payment = $ 93,325.43

Interest amount in first annual payment = $ 850,000 x 0.07 = $ 59,500

Principal paid = $ 93,325.43 - $ 59,500 = $ 33,825.431

Proportion of principal and interest in first annual payment = $ 33,825.431: $ 59,500 = 1: 1.759032

Total payment including principal and interest = $ 93,325.43 x 15 = $ 1,399,881.46

Total interest paid = Total payment – Principal = $ 1,399,881.46 - $ 850,000 = $ 549,881.46

Total principal = $ 850,000

c) For option 2^nd interest rate and hence total interest amount is less as compared to previous one. But need to pay higher annual payment in order to pay the entire loan in a shorter time period. Option 2^nd can be opted as per the capability to pay higher annual payment.