Question

Barney has a balance of $780 on a credit card with an APR of 31.3%, compounded monthly. About how much will he save in interest over the course of a year if he transfers his balance to a credit card with an APR of 19.1%, compounded monthly? (Assume that Barney will make no payments or new purchases during the year, and ignore any possible late-payment fees.)

Answer 1

Barney can save
$119.66
in interest over the course of a year if he transfers his balance to a credit
card with an APR of 19.1%, compounded monthly. The correct answer between all
the choices given is the first choice or letter A.

Answer 2

Barney will save about $119.66.

Explanation:

The compound interest formula is:

A=
`p(1+(r)/(n))^(nt)`

Case 1:

when p = 780

r = 0.313

n = 12

t = 1

Putting the values in formula:

`780(1+(0.313)/(12))^(12)`

A =
`1.36204*780=1062.39`dollars

Interest accured =
`1062.39-780=282.39` dollars

Case 2:

when p = 780

r = 0.191

n = 12

t = 1

Putting the values in formula:

`780(1+(0.191)/(12))^(12)`

A =
`1.20863*780=942.73`dollars

Interest accured =
`942.73-780=162.73` dollars

Now difference in interest in both cases =
`282.39-162.73=119.66` dollars

Hence, Barney will save about $119.66.