Question

You have a $3,000 credit card debt and you plan to pay it off through monthly payments of $75 If you are being charged 15% interest per year, how long to the nearest 0.5 years will it take you to repay your debt? yr

Answer 1

$PV = C \cdot \left[ \frac{1-(1+i)^{-n}}{i} \right]$

$3000 = 75 \times \frac { 1 - \left( 1 + \frac { 0.15 } { 12 } \right) ^ { - n } } { \frac { 0.15 } { 12 } }$

$3000 = 6000 \left( 1 - 1.0125 ^ { - n } \right)$

$0.5= \left( 1 - 1.0125 ^ { - n } \right)$

n= -ln(0.5)/ln(1.0125)

n=55.797630484 months

n= 4.6 years