Question

4. Calculate the payments and amortization table of a 3-year car loan for $12,000 at a 6% rate of interest. The loan will be repaid with three annual payments.

Answer 1

The formula for calculating the payment amount is shown below:

A = P * (r * (1 + r)ⁿ / (1 + r)ⁿ - 1)

where, A is the annual amount. P is the initial loan amount = $12000, r is the rate of interest = 6% and n is the time period = 3 years

Now, putting these values in the above formula, we get,

A = $12000 * (0.06 (1 + 0.06)³ / (1 + 0.06)³ - 1)

A = $12000 * (0.06 (1.06)³ / (1.06)³ - 1)

A = $12000 * (0.06 *1.191016) / (1.191016 - 1)

A = $12000 * (0.07146096 / 0.191016)

A = $12000 * 0.37410981279

A = $4489.31

So, the annual payments will be of $4489.31

Loan amortization schedule:

1st year:

Total payment = $4489.31

Interest = $12000 * 6% = $720

Principal repayment = $4489.31 - $720 = $3769.31

Outstanding principal = $12000 - $3769.31 = $8230.69

2nd year:

Total payment = $4489.31

Interest = $8230.69 * 6% = $493.84

Principal repayment = $4489.31 - $493.84 = $3995.48

Outstanding principal = $8230.69 - $3995.48 = $4235.21

3rd year:

Total payment = $4489.31

Interest = $4235.21 * 6% = $254.11

Principal repayment = $4489.31 - $254.11 = $4235.21

Outstanding principal = $4235.21 - $4235.21 = $0