Jeremy has a balance owing of $4000 on his credit card. The credit-card company charges 18.0% annual interest, compounded monthly.
1.) If Jeremy makes payments of $300 every month, how much will he still owe after making 12 payments?
2.)Determine the monthly payment necessary to have the loan paid off in full after 12 payments.
Not sure if I did part 1 right.
N= 4000(1+0.18/12)^.18/12
= 33422784=$334.23
Part 2 I was going to do $334.23/12=27.85 but it doesn't make sense. Any help would be greatly appreciated.
To solve these questions, we can use the formula for calculating the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r,
where:
- FV is the future value (the balance owing),
- P is the monthly payment amount,
- r is the monthly interest rate, and
- n is the number of payments.
1.) To calculate the balance owing after 12 payments:
Jeremy's balance owing is $4000, and he makes payments of $300 per month. The monthly interest rate is 18.0% / 12 = 1.5%.
FV = $300 * [(1 + 0.015)^12 - 1] / 0.015
= $300 * [1.195618 - 1] / 0.015
= $300 * 0.000618 / 0.015
= $12.54.
Therefore, Jeremy will still owe approximately $12.54 after making 12 payments.
2.) To determine the monthly payment necessary to pay off the loan in full after 12 payments:
We need to solve for P in the following equation:
$4000 = P * [(1 + 0.015)^12 - 1] / 0.015.
Rearranging the equation, we get:
P = $4000 * 0.015 / [(1 + 0.015)^12 - 1]
= $4000 * 0.015 / 0.195618
= $307.42.
Therefore, the monthly payment necessary to pay off the loan in full after 12 payments is approximately $307.42.
Note: In your calculations, it seems like there was an error. The formula you used for part 1 appears to be incorrect, resulting in an inaccurate calculation. For part 2, dividing the balance by the number of payments does not provide the correct answer.