For each of the following loan options (a & b) compute the following values: - a
ID: 2510173 • Letter: F
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.
Explanation / Answer
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 2nd 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 2nd can be opted as per the capability to pay higher annual payment.
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