Question

At what rate per cent per annum will a certain sum of money multiply itself by 55 times in 2 years, the interest being compounded annually? [Give your answer correct to 1 decimal place.]

• A. 644.2
• B. 642.9
• C. 641.6
• D. 638.5

Answer 1

Answer:

C. 641.6

Here's how to solve this compound interest problem:

1. Understand the Compound Interest Formula:

• $A = P (1 + R/100)^n$

  • A = Amount after n years

  • P = Principal (initial sum of money)

  • R = Rate of interest per annum

  • n = Number of years

2. Set up the equation:

• The amount (A) becomes 55 times the principal (P). So, A = 55P.

• The time period (n) is 2 years.

• We need to find the rate of interest (R).

• Substitute the values into the formula:

  • $55P = P (1 + R/100)^2$

3. Solve for R:

• Divide both sides by P:

  • $55 = (1 + R/100)^2$

• Take the square root of both sides:

  • √55 = 1 + R/100

  • 7.416 (approximately) = 1 + R/100

• Subtract 1 from both sides:

  • 7.416 - 1 = R/100

  • 6.416 = R/100

• Multiply both sides by 100:

  • R = 6.416 * 100

  • R = 641.6

4. Round to one decimal place:

• R = 641.6%

Therefore, the rate of interest is approximately 641.6% per annum.