Q:

Four months ago, Máximo Martínez received a loan of $4,346 at an annual rate of 15% and for a term of six months. On this day, he negotiates said debt and agrees to cancel it through two equal payments: the first to be made within a month and the second within four months. If you renegotiate a 12% annual rate; the nominal value, written in integers, of each of the two new documents, is:

Accepted Solution

A:
Okay, let's break this down step-by-step: - Original loan amount: $4,346 - Original term: 6 months - Original interest rate: 15% annually - Interest for 4 months at 15% annually: \*\* Annual interest rate = 15% = 0.15 \*\* Monthly interest rate = 0.15/12 = 0.0125 \*\* Interest for 4 months = Principal * Monthly interest rate * Number of months = $4,346 * 0.0125 * 4 = $174.15 - Total due after 4 months: Principal + Interest = $4,346 + $174.15 = $4,520.15 - This total is being divided into 2 equal payments - New term for each payment is 1 month and 4 months - New (negotiated) interest rate is 12% annually - Calculate monthly interest rate for 12%: Annual rate = 12% = 0.12 Monthly rate = 0.12/12 = 0.01 - Payment 1 (due in 1 month): Principal = $4,520.15/2 = $2,260.08\ Interest for 1 month at 1% = Principal * 0.01 = $22.60 Total due = Principal + Interest = $2,260.08 + $22.60 = $2,282 (rounded to the nearest integer) - Payment 2 (due in 4 months):\ Principal = $2,260.08 Interest for 4 months at 1% = Principal * 0.01 * 4 = $90.40\ Total due = Principal + Interest = $2,260.08 + $90.40 = $2,350 (rounded to the nearest integer) Therefore, the nominal value of each payment, in integers is: Payment 1: $2,282 Payment 2: $2,350