MATH SOLVE

8 months ago

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