Question

Darlene has a balance of $3980 on a credit card with an APR of 22.8%. Paying off her balance in which of these lengths of time will result in her paying the least amount of interest?

A. 8 months
B. 6 months
C. 9 months
D. 5 months

Answer 1

The correct answer is D. 5 months

Explanation:

Balance = P = $3980

Rate (r) = 22.8% ,

n is no. of times interest is calculated in one year n = 1

`Interest=P\cdot (1+(r)/(n* 100))^(n* time)\\\\\textbf{time = t = 8 months = }(8)/(12)\text{ years}\\\\Interest=3980\cdot (1+(22.8)/(1* 100))^{1* (8)/(12)}\\\\Interest=3980* 1.228^{(8)/(12)}\\\\\implies Interest=\$\thinspace 4564.03\\\\\textbf{time = t = 6 months = }(6)/(12)\text{ years}\\\\Interest=3980\cdot (1+(22.8)/(1* 100))^{1* (6)/(12)}\\\\Interest=3980* 1.228^{(6)/(12)}\\\\\implies Interest=\$\thinspace 4410.44`

`\textbf{time = t = 9 months = }(9)/(12)\text{ years}\\\\Interest=3980\cdot (1+(22.8)/(1* 100))^{1* (9)/(12)}\\\\Interest=3980* 1.228^{(9)/(12)}\\\\\implies Interest=\$\thinspace 4642.82\\\\\textbf{time = t = 5 months = }(5)/(12)\text{ years}\\\\Interest=3980\cdot (1+(22.8)/(1* 100))^{1* (5)/(12)}\\\\Interest=3980* 1.228^{(5)/(12)}\\\\\implies Interest=\$\thinspace 4335.60`

Hence, the least amount of interest is paid in time length of 5 months

So, Correct Option is D. 5 months