MATH SOLVE

4 months ago

Q:
# You charged 1,000 on your credit card for Christmas presents. Your credit card company charges you 26% annual interest, compounded monthly. If you make the minimum payments of $25 per month, how long will it take (to the nearest month) to pay off your balance

Accepted Solution

A:

Answer: 94 monthsStep-by-step explanation:You can use the amortization formula for this. A = P(r/12)/(1 -(1 +r/12)^(-n))A is the monthly payment; P is the principal amount; r is the annual interest rate, and n is the number of months. __Filling in the numbers, we can solve for n: 25 = 1000(0.26/12)/(1 -(1+0.26/12)^-n)Multiplying by the denominator and dividing by 25, we have ... 1 -(1+0.26/12)^-n = 1000(0.26)/(12(25)) = 13/15Subtracting 13/15 and adding (1+0.26/12)^-n gives ... 2/15 = (1+0.26/12)^-nTaking logs turns this into a linear equation: log(2/15) = -n·log(1+0.26/12) n = log(15/2)/log(1+0.26/12) = 93.999It would take 94 months, or 7 years 10 months, to pay off the balance._____Your total of payments would be $2,350.