Question

you have a credit card with a balance of $1,467.90 at a 9.5% APR. you pay $400 each month on the due date until the card is paid off. how many months does it take to pay off the card, and what is the total amount paid including interest?

Answer 1

M = L[c(1 + c)^n] / [(1 + c)^n - 1]
M = Fixed Monthly Payment
L = Total Loan Amount
c = Interest rate in decimal PER MONTH where the interest rate is assumed to be compounded monthly. (I am using c instead of i because i is usually per year but here c is per month)
n = Total number of monthly payments

Answer 2

M = 400; L = $1,467.90; c = 0.095/12. Solve for n.

Answer 3

thank you so much for your help

Answer 4

You are welcome. Convert c into a 5 or 6 digit decimal, plug in the numbers and simplify. Eventually you will have to take the log to bring down the n from the exponent position.

Answer 5

ok

Answer 6

Since the balance amount is $1467.90, and each monthly payment is $400, you can calculate each monthly balance.

Start: $1467.90.
1 month of interest: $1467.90 * 0.095 / 12 = $11.62
Interest added to principal: $1467.90 + $11.62 = $1479.52
Pay $400, balance is now 1079.52

New balance: $1079.52
1 month of interest: $1079.52 * 0.095 / 12 = $8.55
Interest added to principal: $1079.52 + $8.55 = $1088.07
Pay $400, balance is now $688.07

New balance: $688.07
1 month of interest: $688.07 * 0.095 / 12 = $5.45
Interest added to principal: $688.07 + $5.45 = $693.51
Pay $400, balance is now $293.51

New balance: $293.51
1 month of interest: $293.51 * 0.095 / 12 = $2.32
Interest added to principal: $293.51 + $2.32 = $295.84
Pay $295.84, balance is now $0

It took 3 payments of $400 and one payment of $295.84 to fully pay the balance.
That means 4 months.

The total interest paid was $11.62 + $8.55 + $5.45 + $2.32 = $27.94
You can also calculate the interest by adding the payments and subtracting the original balance amount: 3 * $400 + $295.84 = $1495.84
$1495.84 - $1467.90 = $27.94

Answer 7

i have no clue i am in 4th grade