## Compound Interest rate

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### Compound Interest rate

IB Mathematical Studies, Financial Mathematics

How can we calculate for what annual rate of interest was paid for an amount of $24,000 to be deposit into an account that compounded quarterly and 2 years later the account totals$29,000?

Thanks
William

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Joined: Mon Jan 28, 2013 8:07 pm

### Re: Compound Interest rate

IB Mathematical Studies, Financial Mathematics, annual rate of interest

The general compounding formula is:
$F=P \cdot (1+ \frac{r}{100})^n$

Where F is the future value of the investment (=$29,000), P the principal (=$24,000), r is the interest rate per compound period (unknown in our case) and n is the number of compounding periods (2*4=8).
Therefore
$29,000=24,000 \cdot (1+ \frac{r}{100})^8=> r=2.3937 \ per \ quarter$ (using solver or graph) and then multiply this number by 4 and get the interest rate per annum $r_{a}=9.57%$

The guidelines for doing this exercise directly to GDC Casio FX-9860 is
TVM -> F2: Compound Interest -> PV=24000, FV=-29000, P/Y=4, C/Y=4, n=8 and then press I% and get the same result (9.57%).

Hope these help!!
nicole

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Joined: Mon Jan 28, 2013 8:10 pm

### Re: Compound Interest rate

Thanks Nicole!
William

Posts: 0
Joined: Mon Jan 28, 2013 8:07 pm