Question

Vinod deposited 30,000 in a bank at 15% per annum. Find the difference in the compound interest
after 2 -1 / 2
years if the interest is compounded yearly and half yearly.​

Answer 1

Answer:

The difference is $-522.18228$.

Step-by-step explanation:

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.

The formula for calculating Compound Interest(CI) is

$CI=P(1+\frac{r}{n})^{nt}-P$

where P = Principal amount

r = rate of interest

n = Compounding frequency per annum

t = time period

Firstly we find the compound interest if the interest is compounded half yearly,

P = 30000

r = 15%

n = 2

t = 2.5

The compound interest is

$CI = 30000(1+\frac{15}{2\times 100})^{2\times 2.5}-30000$

$CI=43068.87979-30000$

$CI=13068.87979$

Now we find the compound interest if the interest is compounded yearly,

P = 30000

r = 15%

n = 1

t = 2.5

The compound interest is

$CI = 30000(1+\frac{15}{100\times 1})^{1\times 2.5}-30000$

$CI = 42546.69751-30000$

$CI=12546.69751$

The difference in compound interest after 2.5 years if the interest is compounded yearly and half yearly is

$12546.69751--13068.87979=-522.18228$.

The CI is more when the interest is compounded half yearly.