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APR confusion

  • 03-09-2015 5:52pm
    #1
    xabi
    Registered Users, Registered Users 2 Posts: 3,006 ✭✭✭


    If 7.5% of 10000 is 750, why does a one year loan of 10000 @ 7.5% APR only cost 397? Shouldn't it cost 750?


Comments

  • #2
    coylemj
    Registered Users, Registered Users 2 Posts: 25,504 ✭✭✭✭coylemj


    Because you're making monthly payments (I make it €866.44) so you don't owe them 10,000 for the whole year i.e. it's a diminishing balance.

    If you borrowed 10,000 on Jan 1st, made no repayments and then came back on the following Jan 1st, you would owe them 10,750.

    Date Balance Interest Payment
    01/01/2015 10,000.00 60.45 866.44
    01/02/2015 9,194.01 55.58 866.44
    01/03/2015 8,383.15 50.68 866.44
    01/04/2015 7,567.39 45.74 866.44
    01/05/2015 6,746.69 40.78 866.44
    01/06/2015 5,921.04 35.79 866.44
    01/07/2015 5,090.39 30.77 866.44
    01/08/2015 4,254.72 25.72 866.44
    01/09/2015 3,414.00 20.64 866.44
    01/10/2015 2,568.20 15.52 866.44
    01/11/2015 1,717.29 10.38 866.44
    01/12/2015 861.23 5.21 866.44
    01/01/2016 -0.00


  • #3
    xabi
    Registered Users, Registered Users 2 Posts: 3,006 ✭✭✭xabi


    Is it 7.9/12 = 0.658 / month on the new balance each month


  • #4
    coylemj
    Registered Users, Registered Users 2 Posts: 25,504 ✭✭✭✭coylemj


    No, you need to calculate the % monthly interest first. Add 1 to the interest rate gives you 1.075 which is the principal plus annual interest. To calculate the monthly interest you get the twelfth root of 1.075 which is 1.006045. That means that the monthly interest applied to the balance is 0.6045%. You apply that rate to the balance at the end of each month, then take away the monthly payment and that's your starter balance for the following month.


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