# Jen takes loan of $12000 at a flat rate of 7.2%p.a. with 36 monthly repayments. Calculate the effective interest rate.

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An effective interest rate reveals the rate a borrower "effectively" pays back when the interest is **compounded** so interest on interest applies.

This question has** not** used compound interest so there is no effective interest rate. For reference purposes , to find an effective interest rate (using the 7.2%) use the formula:

`r=(1+i/n)^n-1` where i=7.2%= 0.072 and n=12 ( working with annual interest rate)` `

`therefore r=(1+0.072/12)^12 -1`

`= 0.074424 times 100`

`therefore r=7.44%` per annum if there was compound interest

**Ans: ****T****his question uses a "flat rate" which infers simple interest, so there is no difference in the rate as effective interest is used for compound interest. **

above answers were incorrect.

total interest paid=12000X7.2X3/100=2592

total money paid 12000+2592=14592

each instalment=14592/36=405

principal in each instalment=12000/36=333.33

interest paid in each instalment=2592/36=72

effective interest rate=(2n/n+1) X flat rate

= (2X36/ 36+1) X7.2 =14.01 %

Correction:

Application to flat rate interest changes the scenario for effective interest rate:

To place the above in context, the effective rate when compared to the flat rate will return a rate much higher than first appears as interest is charged - albeit at a constant rate - on the full outstanding amount regardless of any payments during the course of the loan. It is a simple interest calculation:

P x r x T where P=$12 000 r=7.2% and T = 3 years

We know the interest charged is $2592 over the 3 years

and we know that the total paid is going to be the amount owed plus the interest of $2592

= $14 592 which results in monthly instalments of

$405. 33

As pointed out above the principal portion is $333.33 and

`therefore` the interest portion is $72 pm even though payments are made. Interest is still $72 (simple interest)

To solve, consider if compound interest had been applied and the SAME amount repaid (ie a total of $14592), what would the interest rate be, effectively?

Compounded, the 1st month's int = $473.41

Now deduct the amount towards capital of $333.33

Therefore a difference of $140.08 results, converted to a percentage = 14.008% or 14.01%

**Ans: In context of a loan of $12000 over 3 years at a flat rate of 7.2%, the effective rate is 14.01%**

**Sources:**

Interest

= PrincipleSum x Time x Rate

= $12000 x 36/12 x 7.2%

= $2592

Effective Interest Rate

= $2592 / $12000 x 100%

= 21.6 %