Question

Larson uses his credit card to purchase a new video game system for $519.82. He can pay off up to $225 per month. The card has an annual rate of 15.4% compounded monthly. How much total interest will he pay?

$81.39

$4.72

$11.57

$13.94

Answer 1

help anyone..?

Answer 2

I believe the answer is B.

Answer 3

explain?

Answer 4

Was I right?

Answer 5

not sure, but explain your answer please

Answer 6

I think it is C) $11.57

Amortized loan payment formula:\[\Large R = \frac{ P*i }{ 1 - (1+i)^{-n} }\]R is Regular payment; P is the amount borrowed; i is interest rate per period;
n is number of payments.

P = 519.82; R = 225; i = 0.154/12 = 0.012833; Plug in all the values:\[225 = \frac{ 519.82 * 0.012833 }{ 1 - (1 + 0.012833)^{-n} }\]\[225 = \frac{ 6.671006 }{ 1 - (1.012833)^{-n} }\]\[1 - (1.012833)^{-n} = \frac{ 6.671006 }{ 225 } = 0.0296489\]\[1 - 0.0296489 = 1.012833^{-n}\]\[1.012833^{-n} = 0.9703511\]Take log on both sides:\[-n * \log(1.012833) = \log(0.9703511)\]\[n = -\frac{ \log(0.9703511) }{ \log(1.012833) } = 2.360269\]
n = 2.360269 months. Payments made per month = $225. Total payments made = 225 * 2.360269 = $531.06.
Interest paid = Total payments - Amount borrowed = 531.06 - 519.82 = 11.24

Sp interest paid = $11.24 and the third choice comes the closest.

The reason I was keeping the decimal up to so many places is because these kinds of calculations are sensitive to small variations and we may completely miss the given choices if we round it off early.