Statistics & Applications

Financial Math

Easy

applied

Let $r_e$ denote the effective rate corresponding to the nominal rate r, compounded m times in a year. Let P be the principal and rate per conversion period is $i=\frac{r}{m}$ , then effective rate of interest is:

$r_e = P\left(1+\frac{r}{m}\right)^m - 1$

$r_e = \left(1+\frac{r}{m}\right)^m + 1$

$r_e = \left(1-\frac{r}{m}\right)^m - 1$

$r_e = \left(1+\frac{r}{m}\right)^m - 1$

✅ Correct Option: 4

One unit of principal grows to $\left(1+\frac{r}{m}\right)^m$ in a year under $m$ conversions.

The effective rate is the extra growth over the year, so $r_e=\left(1+\frac{r}{m}\right)^m-1$ .

It is a rate, not an amount, so the principal $P$ does not appear.

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The amount of money needed to ensure for a prize of ₹ 5000 at the begining of each year indefinitely if money is worth 5% compounded annually is:

Let rer_ere​ denote the effective rate corresponding to the nominal rate r, compounded m times in a year. Let P be the principal and rate per conversion period is i=rmi=\frac{r}{m}i=mr​, then effective rate of interest is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Let $r_e$ denote the effective rate corresponding to the nominal rate r, compounded m times in a year. Let P be the principal and rate per conversion period is $i=\frac{r}{m}$ , then effective rate of interest is: