'm trying to figure out the interest. I have a credit card and spent $1,000. I let my sister borrow it and she spent $1,200. I made a payment for $150 and my sister for $300. I finally paid the credit card off at a total of $1,902.20 at a 24% annually interest rate. What would the total interest be for each person based on their purchase total? The card was paid off in 3 months.

Question

'm trying to figure out the interest. I have a credit card and spent $1,000.  I let my sister borrow it and she spent $1,200. I made a payment for $150 and my sister for $300. I finally paid the credit card off at a total of $1,902.20 at a 24% annually interest rate. What would the total interest be for each person based on their purchase total? The card was paid off in 3 months.

anonymous · Answer

bring the payments forward to t=3 months so you can compare them

you didn't specify exactly when the money was spent or when the $150 and $300 payments were made, so let's say the money was spent at t=0 and payments were made 1 month later. (Credit cards usually use average daily balance to compute interest, so the exact day payments are made matters, but let's just ignore that.)

the money your sister owes you at t=3 is 1200*(1.24)^(3/12) - 300*(1.24)^(2/12) = $955.35. The total interest she paid is $955.35 + $300 - $1200 = $55.35

The money you pay to the credit card company is (1000+1200)*1.24^(3/12) - (300+150)*1.24^(2/12) = 1855.12. The interest you paid is (1855.12 - 955.35) + 150 - 1000 = $49.77