Question

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.

Answer 1

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