Simon recently received a credit card with an 18% nominal interest rate. with the card, he purchased a new stereo for $350. the minimum payment on the card is only $10 per month. if simon makes monthly payments of $30, how many months will it be before he pays off the debt? round to the nearest month.

Use the formula of the present value of an annuity ordinary.

The formula is

pv=pmt [ (1 - (1+r/k) ^ (-n)) : (r/k) ]

Pv present value 350

PMT monthly payment 30

R interest rate 0.18

K compounded monthly 12

N number of months?

350=30 [ (1 - (1+0.18/12) ^ (-n)) : (0.18/12) ]

Solve for n

350/30=[ (1 - (1+0.18/12) ^ (-n)) : (0.18/12) ]

((350/30) * (0.18/12)) - 1 = - (1+0.18/12) ^ (-n)

-0.825 = - (1+0.18/12) ^ (-n)

0.825 = (1+0.18/12) ^ (-n)

N=-log (0.825) : log (1+0.18:12)

N=12.9 months round your answer to get 13 months