# Finding weekly interest on loan payments

In order to know how much interest I will be paying on weekly basis, I have this information:

``````Capital: 313 pounds
APR: 48.5%
Payments periods: 104 weeks
``````

How do I know how much interest I'm paying knowing that the weekly amount is fixed. To clarify, this is a pay-to-own service, hence the amount is too low.

• You need to add a `country` or `eurozone` tag because APR means something different in the US than what it means in many other parts of the world. Also, a 48.5% APR would be considered usurious (and likely illegal) in some parts of the world. – Dilip Sarwate Jan 23 at 16:15
• @DilipSarwate 313 EUR is very low so this smells like a payday loan... – MD-Tech Jan 23 at 16:18
• "how much interest I will be paying on weekly basis"? That depends on #1 if you let it sit and grow, or occasionally pay some off, and #2 whether it's simple or compound interest. – RonJohn Jan 23 at 16:21
• Hi, welcome to the site. Is this a real life problem? If so, then it would help to add some more context to the question (in particular, what country this is in), and likely other information would be helpful also as far as how the interest is calculated/amortized. – Joe Jan 23 at 16:24
• Thank you all, I edited the post with the information needed. – nidabdella Jan 23 at 16:39

Assuming that 1) the APR represents the annualized interest rate without compounding and 2) the loan is amortized evenly over the 108 weeks, the payment amount should be:

``````PV  *  r        313   *   .485/52
---------   =   ------------------    = 4.7146
1-(1+r)^-n      1- (i+.485/52)^-52
``````

So the total paid is 4.7146 * 104 = 490.32, 177.32 of which is interest.

If instead the rate is annualized with compounding, the weekly rate would be `1.485^(1/52) - 1` or 0.76% per week. The monthly payment would then be 4.3715, for a total paid of 454.64, 141.64 of which is interest.

However, normally the lender will give you the payment amount. Just multiply that by 104 and subtract off the principal - that will tell you the total interest paid.

Taking 52.1775 weeks per year, to be accurate.

Note, APR in the UK is an effective rate so compounding is considered in calculating the weekly rate `r`. No simply dividing by 52. The difference will be significant for such a high rate.

``````capital        s = 313
weekly rate    r = (1 + 0.485)^(1/52.1775) - 1 = 0.00760705
no. weeks      n = 104

d = weeklypayment
``````

Standard loan equation

$s=\sum_{k=1}^{n}\frac{d}{(1+r)^k}=\frac{d-d(r+1)^{-n}}{r}$

$\therefore d=rs(\frac{1}{(1+r)^n-1}+1)$

``````d = r s (1/((1 + r)^n - 1) + 1) = 4.36634

total payments = n d = 104 * 4.36634 = 454.10

total interest = total payments - capital = 141.10
``````

Which is about £1.36 interest per week.