Question

Wilson has a balance of $890 on a credit card with an APR of 18.7%, 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 12.5%, compounded monthly? (Assume that Wilson will make no payments or new purchases during the year, and ignore any possible late-payment fees.)

Answer 1

890×(1+0.187÷12)^(12)−890×(1+0.125÷12)^(12)
=63.61 saved

Answer 2

Answer:

He will save $ 63.61 ( approx ).

Step-by-step explanation:

Since, the credit card balance formula,

$A=P(1+r)^t$

Where,

P = Original balance

r = rate per period,

t = number of periods,

If P = $ 890,

Annual interest rate = 18.7% = 0.187 ⇒ monthly rate, r = $\frac{0.187}{12}$   ( ∵ 1 year = 12 months )

Number of years = 1 ⇒ months, t = 12,

Thus, the balance after  year,

$A_1=890(1+\frac{0.187}{12})^{12}\approx \ 1071.46$

If Annual interest rate = 12.5% = 0.125 ⇒ monthly rate, r = $\frac{0.125}{12}$  

The balance would be,

$A_2=890(1+\frac{0.125}{12})^{12}\approx \ 1007.85$

Since,

$A_1-A_2=1071.46-1007.85=\ 63.61$

Hence, he will save $ 63.61 ( approx ).