The Bennetts spend $10,000.00 on a home improvement project. They make the purchase with a credit card that has a 9% APR. They decide to make $150.00 monthly payments.
How many months will it take to pay off the credit card balance?
Can someone show me a step by step on how to solve or a formula
Wow, first of all, where do you find a credit card that charges 9% ???
This is the formula:
Present Value = payment( 1 - (1+i)^-n)/i
where i is the interest rate per period expressed as a decimal (in this case period is 1 month)
n is the number of interest periods
so
i = .09/12 = .0075
n = ?? (we don't know that)
payment = 150
PV = 10000
10000 = 150(1 - 1.0075^-n)/.0075
75 = 150(1 - 1.0075^-n)
1/2 = 1 - 1.0075^-n
1.0075^-n = 1/2
we know have to use logs, take log of both sides and use log rules
-n log 1.0075 = log .5
-n = log .5/log 1.0075 = -92.76...
n = appr 93 interest periods, which were months
I will take 92 full payments of 150, plus a partial final payment in the 93rd month
Well, let's calculate how many months it will take the Bennetts to pay off their credit card balance using some clown logic!
Step 1: Take a break before starting. Eating a clown-sized sandwich might help.
Step 2: Find a comfortable spot to do your math. The couch is always a clown's favorite place to concentrate.
Step 3: Take a deep breath and look at the numbers. $10,000.00 debt at 9% APR.
Step 4: Calculate the monthly interest rate. Multiply the APR by the debt. Carry the balance on your clown nose.
9% x $10,000 = $900 monthly interest rate. Ouch!
Step 5: Subtract the monthly payments. This will determine how much of the debt you'll be tackling each month.
$150 - $900 = -$750.00
Wait... Negative money? That doesn't seem right! Looks like the Bennetts are in for an interesting journey.
Step 6: Keep making those monthly payments and watch the balance grow bigger and bigger! This is what clowns call "reverse magic."
Step 7: Eventually, the hilarity stops. When you finally reach a negative balance larger than the debt, you can safely consider it paid off.
In this case, $10,000 / $750 = approximately 13.33 months.
But remember, this is just an estimate! In reality, with the interest piling up, it may take the Bennetts a bit longer to fully repay the debt. So, don't be surprised if you see a clown hanging around a while longer.
And that's how a clown solves financial problems; with laughter and a dash of absurdity!
To calculate how many months it will take to pay off the credit card balance, we can use the formula for the number of periods (n) needed to pay off a loan with equal monthly payments.
The formula is:
n = -(log(1 - (r * P) / A) / log(1 + r))
Where:
n = number of periods (in this case, the number of months)
r = monthly interest rate (APR divided by 12 months)
P = monthly payment
A = initial credit card balance
Let's calculate the number of months step by step:
1. Convert the APR to a monthly interest rate:
Monthly interest rate (r) = 9% / 12 months
r = 0.09 / 12
r = 0.0075
2. Substitute the given values into the formula:
n = -(log(1 - (0.0075 * 10000) / 150) / log(1 + 0.0075))
3. Simplify the equation inside the logarithm:
n = -(log(1 - 0.50) / log(1.0075))
4. Calculate the numerator of the equation:
1 - 0.50 = 0.50
5. Calculate the logarithm:
log(0.50) ≈ -0.3010
6. Substitute the values into the formula:
n = -(-0.3010) / log(1.0075)
7. Simplify:
n = 0.3010 / 0.0009
8. Calculate the result:
n ≈ 334.4
Therefore, it will take approximately 334.4 months to pay off the credit card balance using monthly payments of $150. Since we cannot have a fraction of a month, we round up to the next whole month.
Thus, it will take 335 months to pay off the credit card balance.
To calculate the number of months it will take to pay off the credit card balance, you can use the formula for calculating the number of periods required to repay a loan with fixed monthly payments, which is also known as the "loan amortization formula."
Here's the step-by-step process to calculate the number of months:
Step 1: Write down the given information:
Principal amount (P) = $10,000.00
Monthly payment (A) = $150.00
Annual Percentage Rate (APR) = 9%
Step 2: Convert the annual interest rate to a monthly interest rate:
Monthly interest rate (r) = APR/12 = 9%/12 = 0.0075
Step 3: Substitute the given values into the formula:
n = -log(1-[(P*r)/A]) / log(1+r)
Step 4: Calculate the number of months:
n = -log(1-[(10000*0.0075)/150]) / log(1+0.0075)
Step 5: Compute the value inside the logarithm:
1-[(10000*0.0075)/150] = 0.95
Step 6: Calculate the number of months:
n = -log(0.95) / log(1+0.0075)
Step 7: Use a calculator to solve the equation:
n ≈ 68.98
Step 8: Round up to the nearest whole number, as you cannot have a fraction of a month:
n = 69
Hence, it will take approximately 69 months to pay off the credit card balance by making $150.00 monthly payments.