Question

Find the compound interest on R 50,000 at 16% per annum for 2 years,

compounded​

Answer 1

${\pmb{\underline{\sf{ Required \ Solution ... }}}}$

• Principal = ₹ 50000
• Rate (r) = 16%
• Time (t) = 2 years

We have to calculate the Compound Interest but for this we've to find the Amount obtained as:-

$\circ \ {\pmb{\underline{\boxed{\sf{ Amount = P \left( 1 + \dfrac{r}{100} \right) ^n }}}}} \\ \\ \\ \colon\implies{\sf{ 50000 \left( 1 + \dfrac{16}{100} \right) ^2 }} \\ \\ \\ \colon\implies{\sf{ 50000 \left( \cancel{ \dfrac{116}{100} } \right)^2 }} \\ \\ \\ \colon\implies{\sf{ 50000 \left( \dfrac{29}{25} \right)^2 }} \\ \\ \\ \colon\implies{\sf{ \cancel{50000} \times \dfrac{29}{ \cancel{25} } \times \dfrac{29}{ \cancel{25} } }} \\ \\ \\ \colon\implies{\sf{ 80 \times 841 }} \\ \\ \\ \colon\implies{\sf{ 67280 }}$

So, The amount of the transaction is ₹ 67280.

We also know that:-

$\colon\implies{\sf{ Interest = Amount - Principal }} \\ \\ \colon\implies{\sf{ 67280 - 50000 }} \\ \\ \colon\implies{\sf{ Rs. \ 17280_{(Compound \ Interest )} }}$

Hence,

The Compound Interest of the transaction will be ₹17280 .

Answer 2

Solution!!

The concept of compound interest has to be used here. The principal, rate of interest and time is given. We have to find the compound interest and the amount.

We can find it with formula and without formula too.

Principal (P) = Rs 50,000

Time (n) = 2 years

Rate of interest (R) = 16%

Amount = P(1 + (R/100))ⁿ

Amount = 5000(1 + (16/100))²

Amount = 5000(116/100)²

Amount = 5000(29/25)²

Amount = 5000 × (29/25) × (29/25)

Amount = 80 × (29) × (29)

Amount = Rs 67,280

Compound interest (CI) = Amount - Principal

CI = Rs 67,280 - Rs 50,000

CI = Rs 17,280

Now let's do this without the formula.

For 1st year

Principal (P) = Rs 50000

Rate of interest (R) = 16%

Time (T) = 1 year

Interest = (P × R × T)/100

Interest = (50000 × 16 × 1)/100

Interest = 500 × 16

Interest = Rs 8000

Amount = Principal + Interest

Amount = Rs 50000 + Rs 8000

Amount = Rs 58000

For 2nd year

The amount in the 1st year will be the principal in the 2nd year.

Principal (P) = Rs 58000

Rate of interest (R) = 16%

Time (T) = 1 year

Interest = (P × R × T)/100

Interest = (58000 × 16 × 1)/100

Interest = 580 × 16

Interest = Rs 9280

Amount = Principal + Interest

Amount = Rs 58000 + Rs 9280

Amount = Rs 67,280

Compound interest (CI) = Interest in the 1st year + Interest in the 2nd year

CI = Rs 8000 + Rs 9280

CI = Rs 17,280