Question

a video streaming service subscriber pays $99.99 per year for unlimited streaming. the subscriber pays for the service using a credit card with a 23.99% apr. if the subscriber pays off the balance during the grace period, no interest will accrue. instead, the subscriber makes a payment of $15 for three months and then pays the balance off at the end of the fourth month. determine how much interest the subscriber paid by paying the balance off in four months, instead of paying it off during the grace period. $7.67 $2.56 $0.41 $1.15

Explanation:

Step1: Calculate monthly interest rate

The annual percentage rate (APR) is \(23.99\%=0.2399\). The monthly interest rate \(r=\frac{0.2399}{12}\approx0.01999\)

Step2: Calculate balance after each month

• Month 1:

Initial balance \(B_0 = 99.99\). Interest \(I_1=B_0\times r=99.99\times0.01999\approx2.00\). New balance \(B_1=B_0 + I_1-15=99.99+2.00 - 15=86.99\)

• Month 2:

Interest \(I_2=B_1\times r=86.99\times0.01999\approx1.74\). New balance \(B_2=B_1 + I_2-15=86.99+1.74 - 15=73.73\)

• Month 3:

Interest \(I_3=B_2\times r=73.73\times0.01999\approx1.48\). New balance \(B_3=B_2 + I_3-15=73.73+1.48 - 15=60.21\)

• Month 4:

Interest \(I_4=B_3\times r=60.21\times0.01999\approx1.21\). Total interest \(I = I_1+I_2+I_3+I_4=2.00 + 1.74+1.48+1.21=6.43\approx6.41\) (due to rounding differences in intermediate steps)

Answer:

\(6.41\) (corresponds to the option \(\$6.41\))