A sum of Rs 625 becomes Rs 1296 in 1 year, if the rate is compounded q

1.	A sum of Rs 625 becomes Rs 1296 in 1 year, if the rate is compounded quarterly. Find the rate percent per annum.1. 20% per annum2. 15% per annum3. 40% per annum4. 80% per annum
Answer» Correct Answer - Option 4 : 80% per annum Given: Principal = Rs 625, Amount = Rs 1296, Time period = 1 year or 4 quarters Formula Used: A = P{1 + (r/100)}n where, A = Amount, P = Principal, r = Rate% and n = Time or number of periods Calculation: Here, A = P{1 + (r/100)}4 ⇒ 1296 = 625 × {1 + (r/100)}4 ⇒ 1296/625 = {1 + (r/100)}⁴ ⇒ (6/5)⁴ = {1 + (r/100)}⁴ When LHS = RHS with same power then bases should be equal. ⇒ (6/5) = 1 + (r/100) ⇒ (6/5) - 1 = r/100 ⇒ 1/5 = r/100 ⇒ r = 20% As we have taken time period as 4 quarters, so the rate we calculated is per quarter. So Rate % per annum = 20 × 4 = 80% per annum. ∴ The Rate percent per annum is 80%.

A sum of Rs 625 becomes Rs 1296 in 1 year, if the rate is compounded quarterly. Find the rate percent per annum.1. 20% per annum2. 15% per annum3. 40% per annum4. 80% per annum

Answer» Correct Answer - Option 4 : 80% per annum

Given:

Principal = Rs 625,

Amount = Rs 1296,

Time period = 1 year or 4 quarters

Formula Used:

A = P{1 + (r/100)}n

where, A = Amount, P = Principal, r = Rate% and n = Time or number of periods

Calculation:

Here,

A = P{1 + (r/100)}4

⇒ 1296 = 625 × {1 + (r/100)}4

⇒ 1296/625 = {1 + (r/100)}⁴

⇒ (6/5)⁴ = {1 + (r/100)}⁴

When LHS = RHS with same power then bases should be equal.

⇒ (6/5) = 1 + (r/100)

⇒ (6/5) - 1 = r/100

⇒ 1/5 = r/100

⇒ r = 20%

As we have taken time period as 4 quarters, so the rate we calculated is per quarter.

So Rate % per annum = 20 × 4 = 80% per annum.

∴ The Rate percent per annum is 80%.

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