Question

If the effective rate of interest compounded quarterly is 16 %, then the nominal rate of interest is​

Answer 1

Answer:

The nominal rate of interest is $16.99\%$.

Step-by-step explanation:

The formula for compound interest is :

$CI=P*[1+\frac{r}{100} ]^t$

where P is the principal

r is the rate of interest

t is the time

Here, the interest is compounded quarterly.

Hence, the rate of interest is $\frac{r}{4}$

The quarterly rate of interest is given as : $\frac{16}{4}=4\%$

The rate of interest :

$P*[1+\frac{4}{100} ]^4$

$=P*(\frac{104}{100})^4\\\\ =P*(\frac{26}{25})^4\\\\=P*1.1699$

The effective rate of interest is :

$1.1699P-P=0.1699P$

The nominal rate of interest is $16.99\%$.

Compound interest:

The interest on a loan or deposit that is calculated using both the initial principle and the interest charges from prior periods is known as compound interest (or compounding interest).

Compound interest, often known as "interest on interest," is said to have started in 17th-century Italy.

It will cause a payment to grow more quickly than simple interest, which is computed just on the principal amount.