Question

Dave has a credit card balance of $20,000, which carries an APR of 20%. He pays $400 per month towards retiring the balance. How long will it take Dave to reduce the balance to $0?

Answer 1

Answer:

The answer to the question is

it will take Dave 108.399 months or 9.03 years to reduce the balance to $0

Step-by-step explanation:

To solve the question, we note that

Balance cresdit = $20,000

APR = 20%

PMT = $400 per month we have

$A = P(1+\frac{r}{n} )^{nt}$ and

$A=P\frac{r(1+r)^n}{(1+r)^n-1}$ where r = 20 %÷12

P  = $20000 and A = 400

Therefore we have$400 = 20000\frac{\frac{0.2}{12} (1+\frac{0.2}{12})^n }{(1+\frac{0.2}{12})^n-1}$

which gives 6/5=$\frac{ (\frac{61}{60})^n }{(\frac{61}{60})^n-1}$

= $(\frac{61}{60})^n$ = 6 that is ln $(\frac{61}{60})^n$ = ln (6) or n = $\frac{ln(6)}{ln(\frac{61}{60}) }$ = 108.399 months = 108.399/12 or 9.03 years