# 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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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:

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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:  This 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.

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Interest

= PrincipleSum x Time x Rate

= \$12000 x 36/12 x 7.2%

= \$2592

Effective Interest Rate

= \$2592 / \$12000 x 100%

= 21.6 %

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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 %