Question

You have decided to apply for a bank loan to equip your company's laboratory, for which it requires $ 2,000,000.00, currently the company has retained earnings of $ 500,000, which it will use to give the equipment down payment. The rest will be financed with a 10-year loan at a rate of 12% per year, capitalized monthly. The bank requests to make constant monthly payments (the same payment at the end of each month, during the 120 month duration of the credit). What amount will you pay exclusively for interest (debt service) in the 3rd month of the credit? (The currency is Mexican pesos)

Answer 1

After down-payment, the remaining amount is = 2,000,000 - 500,000 = 1,500,000. Since the rate is 12% per year, it will be 1% each month. Let the monthly payment be A. Hence, writing the present value equation, we have:

1500000 = A x (1/1.01^1 + 1/1.01^2 + ... + 1/1.01^120)

Hence, A = 21520.64.

Hence, in the first month, the total interest payment was = 0.01 x 1500000 = 15000. So, the principal payment in the first payment was = 21520.64 - 15000 = 6520.64. So, the remaining principal was = 1,500,000 - 6520.64 = 1493479.36. In the second year, the interest payment would be = 0.01 x 1493479.36 = 14934.7936. Hence, the principal payment would be = 21520.64 - 14934.7936 = 6585.84. Hence, the principal remaining would be = 1493479.36 - 6585.84 = 1486893.52. Hence, the interest for the third month will be = 0.01 x 1486893.52 = 14868.9352.