Question

Joan Messineo borrowed $10,000 at a 17% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments.

a. Calculate the annual, end-of-year loan payment

b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage of time.

Answer 1

If the loan amount is P, rate on interest (monthly is r, and loan term is n the EMI will be

EMI = P*r[(1 +r)^n]/ [(1+ r)^n- 1]

Where,

              Loan amount (P) = $10000

                Time (n) = 3

               Interest rate [r] = 17% /period

Let's put all the values in the formula to calculate EMI

EMI = 10000*0.17[(1 +0.17)^3]/ [(1+ 0.17)^3- 1]

        = 1700[(1.17)^3]/ [(1.17)^3- 1]

        = 1700[1.601613]/ [1.601613- 1]

        = 1700[1.601613]/ [0.601613]

        = 1700[2.6621981240432]

        = 4525.74

So EMI will be $4525.74

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EMI	Loan balance	EMI	Interest (Loan balance* interest rate)	Principle (EMI - Interest)	Loan balance (Loan - principle)
1	10000	4525.74	1700.00	2825.74	7174.26
2	7174.26	4525.74	1219.62	3306.12	3868.14
3	3868.14	4525.74	657.58	3868.16	0.0

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Interest in dependent on Loan balance, and each EMI has some portion of principle, so principle is reducing after every EMI, so interest expense is also decreasing.

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