Question

Problem 1 - Amortizing a Loan

Jason takes out a loan L of 3000 dollars to buy a car at an annual effective rate of interest of 6%. He repays the loan by making annual payments at the end of each year for 10 years.

a) The amount of Jason's annual payment is R=______

b) The amount of interest Jason paid in the 1st payment is I1=iL_________

c) The amount of principal repaid in the 1st payment is P1=R−I1_______

d) The outstanding loan balance at the end of the 1st year just after the 1st payment is paid is B1=L−P1=___________

e) The amount of interest Jason paid in the 2nd payment is I2=iB1__________

f) The amount of principal repaid in the 2nd payment is P2=R−I2=_________

g) The outstanding loan balance at the end of the 2nd year just after the 2nd payment is paid is B2=B1−P2=

Answer 1

1. Formula for calculating annual payments

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

Where A = Annual payments

P = Principle loan taken

R = Rate of interest

N = total number of payments

A = 3000 [0.06 (1+0.06) ^10 / (1+0.06) ^ 10-1]

A = $407.6

2.Amount of interest 1^st year = $3000*6% = $180

3.Amount of principle 1^st year = $407.6 – 180 = $227.6

4.Outstanding loan balance at the end of 1^st year = $3000 – 407.6 = $2,592.4

5.Amount of interest 2nd year = ($3000 – 227.6)*6% =$166.34

6.Amount of principle 2^nd year = $407.6 – 166.34 = $241.26

7.Outstanding loan balance at the end of 2^nd year = $2,592.4 – 407.6 = $2,184.8

I hope this will help you. If requires clarification, you may comment below.