megan borrows £5000 to buy a cat at a rate of 8% over 3 years. how much does she have to pay over the three years? if she pays the loan back every month over three years ,how much is her monthly payment?
if there was an arrangement fee of £500 for the initial loan, calculate the APR for the loan
i = .08/12 = .006666...
n = 3(12) = 36
let the monthly payment be p
p(1 - 1.00666...^-36)/.006666.. = 5000
p = 156.68
Is the second part a new question?
Not sure how this "arrangement" fee works in.
Do the payments change?
Clearly the interest rate is not 8%, or else it would not have been asked for
Please clarify
thank very much for you help really thank you cuz i did't understand anything of the question thank you for your help. its the same question you can use the same information
To calculate the total amount Megan has to pay over the three years, we need to calculate the interest first and then add it to the principal loan amount.
Step 1: Calculate the interest
Interest = Principal x Rate x Time
Principal = £5000
Rate = 8% (8/100 = 0.08)
Time = 3 years
Interest = £5000 x 0.08 x 3
Interest = £1200
Step 2: Calculate the total amount to be paid
Total amount = Principal + Interest
Total amount = £5000 + £1200
Total amount = £6200
Therefore, Megan has to pay £6200 over the three years.
To calculate her monthly payment, we need to divide the total amount by the number of months in three years.
Number of months = 3 years x 12 months
Number of months = 36 months
Monthly payment = Total amount / Number of months
Monthly payment = £6200 / 36
Monthly payment ≈ £172.22 (rounded to two decimal places)
So, Megan's monthly payment is approximately £172.22.
Now let's calculate the APR (Annual Percentage Rate) for the loan, taking into account the arrangement fee of £500.
Step 1: Calculate the total amount of the loan including the arrangement fee
Total loan amount = Principal + Arrangement fee
Total loan amount = £5000 + £500
Total loan amount = £5500
Step 2: Calculate the interest rate for the loan, considering the arrangement fee
Rate = (Total interest / Total loan amount) x (1 / Time)
Total interest = £1200 (from the earlier calculation)
Total loan amount = £5500
Time = 3 years
Rate = (£1200 / £5500) x (1 / 3)
Rate ≈ 0.0727 (rounded to four decimal places)
Step 3: Calculate the APR
APR = Rate x 100
APR ≈ 0.0727 x 100
APR ≈ 7.27%
Therefore, the APR for the loan, including the arrangement fee, is approximately 7.27%.