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# Identify in which type of interest rate is applied to the original principal and any accumulated interest?(a) Simple interest(b) Compound interest(c) Annual interest(d) Half-yearly interest

Last updated date: 20th Jun 2024
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Hint: In the above question, we have to mark the option on which interest rate is applied to both the original principal and any accumulated interest. So, we have to check each option separately and see whether the interest rate on that particular type of interest is applied on both the original principal and accumulated interest.

Complete step-by-step solution:
We have to check in which option, the interest rate is applied on both the original principal and accumulated interest.
Checking option (a),
In simple interest, the interest rate is applied on the original principal only and the formula for simple interest is:
$S.I.=\dfrac{P\times R\times T}{100}$
In the above formula, you can see that “P” stands for principal, “R” stands for rate, and “T” stands for the time in years. From the above formula also, you can see that interest rate “R” is applied to the principal only, not on the accumulated interest (i.e. simple interest).
Hence, this option is incorrect.
Checking option (b),
In compound interest, the rate of interest is applied to the original principal and on the interests of the previous periods. To have a better understanding of this statement, we are showing the formula for the compound interest as follows:
$C.I.=P{{\left( 1+\dfrac{r}{100} \right)}^{T}}-P$
In the above formula, “P” stands for principal, “r” stands for the interest rate, and “T” stands for the time period in years. As you can see from the above formula, that rate of interest depends upon the original principal and the accumulated interests of previous periods.
Hence, the interest rate on compound interest depends upon the original principal and the accumulated interests. Hence, option (b) is the correct option.
Checking option (c),
Annual interest is the yearly interest so here the interest rate only depends on the original principal and for the time period of 1 year.
Hence, this option is also incorrect because the interest rate depends only on the original principal, not on accumulated interests.
Checking option (d),
Half-yearly interest is the interest that occurs after half a year so here the interest rate depends only on the original principal and not on the accumulated interests.
Hence, this option is also incorrect because the interest rate depends only on the original principal, not on accumulated interests.
From the above scrutiny of the options, we have found that the correct option is (b).

Note: You might get confused with the interest rate and interest. The key to getting out of this confusion is interest is the amount that you get when a certain interest rate is incurred on the principal. You can also remember that interest rate is always given in the percentage and interest is just a number.
The take-home message from this problem is that in simple interest, the interest rate is applied only on the original principal but in compound interest, the interest rate is applied to the original principal and on the interests of previous periods. Compound interest is like interest on interest.