To determine the annual payment for a loan of 50000 at an interest rate of 12% over a three-year period, we can use the formula for the annuity payment. The formula is:
Pmt = (PV * r) / (1 – (1 + r)^-n)
Where:
- Pmt = annual payment
- PV = present value of the loan (50000)
- r = interest rate per period (12% or 0.12)
- n = number of periods (3 years)
First, we convert the interest rate to a decimal:
r = 0.12
Next, we substitute the values into the formula:
Pmt = (50000 * 0.12) / (1 – (1 + 0.12)^-3)
Calculating the denominator:
(1 – (1 + 0.12)^-3) = (1 – (1.12)^-3) ≈ 0.2768
Now calculating the payment:
Pmt = (50000 * 0.12) / 0.2768 ≈ 21787.12
So, the annual payment will be approximately $21,787.12.
Next, to find the interest payment for the second year, we first need to determine the loan balance at the start of the second year.
At the end of the first year, the interest accrued on the loan balance of 50000 is:
Interest Year 1 = 50000 * 0.12 = 6000
Therefore, the total amount owed at the end of the first year is:
Loan Balance Year 1 = 50000 + 6000 – 21787.12 ≈ 27812.88
Now, for the second year’s interest payment:
Interest Year 2 = 27812.88 * 0.12 ≈ 3337.55
Thus, the interest payment for the second year will be approximately $3,337.55.