Question

Find the ratio of compound interest half-yearly to simple interest for the principal 10,000 and the rate of interest is 20%, for 1 year.​

Answer 1

Answer:

Principal amount is Rs.10,000.

6% is the rate for 1stand 2nd year and 9% for the 3rd year.

For half yearly we half the rate so 3% for 1st and 2nd year and 4.5% for 3rd year and double the time period so 6 half yrs.

Compound interest=total amount- principal amount

=>10,000(1+3100)4(1+9200)2−10,000

=>Rs.2290

Answer 2

Answer:

The ratio of Compound Interest half-yearly to the Simple interest   = 21:20

Step-by-step explanation:

Given

Principal = 10,000

Rate of interest = 20%

Time period = 1 year

To find:

The ratio of  compound interest half-yearly to the simple interest

Solution:

Recall the formulas

Compound interest  C. I = $P(1+\frac{r}{100})^n - P$, where P is the principal, r is the rate of interest and n is the period

To calculate the compound interest half yearly, the rate of interest is halved and the number of years is doubled in the above formula

Then the above formula becomes,

C.I = $P(1+\frac{r/2}{100})^{2n} - P$

Simple interest = S.I = $\frac{PTR}{100}$

Substituting the values we get,

$C.I = P[(1+\frac{r/2}{100})^{2n} - 1]\\\\= P[(1+\frac{10}{100})^{2} - 1]\\\\= P[(\frac{100+10}{100})^2 - 1]$

$= P[(\frac{100+10}{100})^2 - 1]\\\\= P[(\frac{11}{10)})^2 - 1]\\\\\= P[1.1^2 - 1]\\\\= P(1.21 - 1)\\= 0.21P$

C.I  = 0.21P

Simple Interest = $\frac{PX1X20}{100}$

= 0.2P

The ratio of Compound Interest half-yearly to the Simple interest   = $\frac{0.21P}{0.2P} = \frac{21}{20}$ = 21:20

Answer:

The ratio of Compound Interest half-yearly to the Simple interest   = 21:20

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