Question

You borrow $10000 for a capital equipment at 6% interest. If you plan to pay back
2000/yr how long will it take to pay off the debt ? What is the amount of the final payment?

Answer 1

This is the present value of annuity calculation:

Annual payment = A = $2,000

Present value = PV = $10,000

r = rate of interest = 0.06

n = Number of years =?

By the formula as below:

PV = (A/r) {1 – (1 + r) ^ (-n)}

10,000 = (2,000/0.06) {1 – (1 + 0.06) ^ (- n)}

10,000 = 33,333.33 × {1 – (1.06) ^ (- n)}

10,000 / 33,333.33 = 1 – (1/1.06^n)

0.3 = 1 – (1/1.06^n)

0.3 – 1 = - (1/1.06^n)

- 0.7 = - (1/1.06^n)

By cancelling the minus sign from both the sides,

0.7 = 1 / 1.06^n

1.06^n = 1/0.7

1.06^n = 1.42857

n = In (1.42857) / In (1.06)

   = 0.35667 / 0.05826

   = 6.12

   = 6 rounded

Answer: it takes 6 years to pay off.

Principal amount (final payment) = A × (1 – r)

                                                      = 2,000 × (1 – 0.06)

                                                      = 2,000 × 0.94

                                                      = $1,880 (Answer)