Sheila bought a new computer for $2000 and has agreed to finance it at 12% interest with a $100 payments each month. When she makes her first payment next month, how much will she pay for interest alone?
(2,000 * 0.12) / 12 = ?
I will assume the interest is compounded monthly, so the monthly rate is 1%
1% of 2000 = $20
so of the first payment of $100, $20 will go to interest and $80 will be actual repayment.
of course the next month, her interest will be less:
balance = 2000-80 = 1920
.01(1920) = $19.20
etc
An interesting question:
How many full payments of $100 will there be, and what will be the partial payment made one month after the last full payment of $100 ?
rate per month = .01 agreed = r
Luckily they only ask for the first month so it is 0.01 * 20 as Reiny and Ms. Sue said.
Later months get more complicated and it is like paying off a mortgage with the term unknown but the rate and payment known.
Payment = principal value [ r / {1-(1+r)^-n } ]
100 = 2000 [ .01 / {1 - (1.01)^-n } ]
5 = 1/ {1 - (1.01)^-n }
.2 = 1 - (1.01)^-n
.8 = 1.01^-n
log .8 = -n log 1.01
n = 22.4 months :)
so over the almost two years pay 2240 total :)
To find out how much Sheila will pay for interest alone, we need to calculate the interest portion of each payment.
First, let's calculate the interest portion of the first payment using the formula:
Interest = Principal x Rate
Where:
Principal = amount Sheila owes initially ($2000)
Rate = annual interest rate (12%)
To calculate the monthly interest rate, we divide the annual interest rate by 12:
Monthly interest rate = (Rate/100) / 12
Let's calculate the monthly interest rate:
Monthly interest rate = (12/100) / 12 = 0.01
Now, we can calculate the interest portion of the first payment:
Interest = Principal x Monthly interest rate
Interest = $2000 x 0.01 = $20
Therefore, Sheila will pay $20 for interest alone when she makes her first payment next month.