A sum invested in a fixed interest bank deposit account increased in value by 40% over 5 years.

The problem involves calculating the future value of a sum invested in a fixed interest bank deposit account that experiences a 40% increase over 5 years.

1. ### Break Down the Problem

• Identify the initial investment (commonly denoted as $P$).
• Determine the total increase after 5 years which is given as 40%.
• Calculate the future value ($F$) after 5 years.

2. ### Relevant Concepts

• The formula to calculate the future value of an investment is given by: $F = P(1 + r)^t$ where:
  • $F$ = future value
  • $P$ = principal amount (initial investment)
  • $r$ = annual interest rate (as a decimal)
  • $t$ = time in years

3. ### Analysis and Detail

• From the problem, we understand that the total increase is 40% over 5 years, meaning: $F = P + 0.40P = 1.40P$
• Relating this to our formula, we can express the 5-year increase as follows: $1.40P = P(1 + r)^5$
• Dividing both sides by $P$ (assuming $P \neq 0$): $1.40 = (1 + r)^5$
• To find $r$, we need to take the fifth root of both sides: $1 + r = (1.40)^{1/5}$ $r = (1.40)^{1/5} - 1$

4. ### Verify and Summarize

• Now, let's calculate $(1.40)^{1/5}$: $(1.40)^{1/5} \approx 1.0672$
• Thus: $r \approx 1.0672 - 1 \approx 0.0672$ which is about 6.72% per annum.

Final Answer

The annual interest rate on the fixed interest bank deposit account is approximately 6.72%.