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Answer :
Miriam will be able to pay off the DVD player in approximately 13.9 months, which is significantly quicker than making just the minimum payments.
Initially, Miriam bought a DVD player for $250 using her credit card with an APR of 12%. The credit card statement indicated that she only needed to make a minimum monthly payment of $15.
To determine how long it would take for Miriam to pay off the DVD player if she only made the minimum payments, we can use the formula for the number of months to pay off a debt:
N = -(log(1 - (B/M) * (1 + r)) / log(1 + r))
Where:
N is the number of months to pay off the debt,
B is the initial balance ($250),
M is the monthly payment ($15),
and r is the monthly interest rate (APR divided by 12, so 12%/12 = 1%).
Plugging in the values:
N = -(log(1 - (250/15) * (1 + 0.01)) / log(1 + 0.01))
N ≈ 32.6 months
Therefore, it would take Miriam approximately 32.6 months to pay off the DVD player if she only made the minimum monthly payments.
If Miriam decides to pay twice the minimum monthly payment ($30 per month), we can calculate the new time to pay off the debt using the same formula:
N = -(log(1 - (250/30) * (1 + 0.01)) / log(1 + 0.01))
N ≈ 13.9 months
By paying twice the minimum monthly payment, Miriam will be able to pay off the DVD player in approximately 13.9 months, which is significantly quicker than making just the minimum payments.
Therefore, paying more than the minimum payment each month will significantly reduce the time it takes for Miriam to pay off the DVD player.
Learn more about DVD player from below link
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