Question

Today, you borrowed $3,200 on a credit card that charges an interest rate of 12.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $60

Answer 1

Answer:

It will take me = 30.99 years to pay-off the borrowed amount paying $60.00 every month

Explanation:

SOLUTION:

Using the Formula: A = P(1+r/n)${nt}$

Where:

A= $60.00;

P = $3,200.00;

r = 12.9%;

n = 12

t =?

Substituting the values into the Formula =

$60 = $3,200(1 + 12.9%/12)${12t}$

= $60 = $3,200(1 + 12.9%/12)${12t}$

= $60.00 = $3,200.00 (1 + 0.129/12)${12t}$

= $60.00 = $3,200.00 (1 + 0.01075 )${12t}$

= $60.00 = $3,200.00 (1.01075 )${12t}$

= $60.00/$3,200.00 = $3,200.00 (1.01075 )${12t}$/$3200.00

= 0.01875 = (1.01075)$12t$

= Using the law of logarithm

= log$A^{N}$ = Nlog A

=12tlog(1.01075) = log0.01875

= 12log(1.01075)/(1.01075) = log0.01875/log(1.01075)

=  12t = log(0.01875)/log1.01075

= 12t = 1.7270/0.04644

Divide 12 by both sides

=12t/12 = 371.88774/12

t= 30.9898

∴ 30.99 years

It will take me = 30.99 years to pay-off the borrowed amount paying $60.00 every month