Question

A certain amount of money at compound interest grows to 66,550 in 3 years and 73,205 in 4 years. The rate percent per annum is:

• A. 0.1
• B. 0.09
• C. 0.05
• D. 0.11

Answer 1

The Correct Option is A

To find the rate of compound interest, we use the concept of compound interest and the given amounts at two different times. We have:

• The amount grows to 66,550 in 3 years. 
• The amount grows to 73,205 in 4 years.

The formula for compound interest is given by:

\(A = P(1 + r)^n\)

Where:

• \(A\) is the amount after time \(n\)
• \(P\) is the principal amount
• \(r\) is the rate of interest per annum
• \(n\) is the number of years

We are given \(A = 66,550\) for \(n = 3\) and \(A = 73,205\) for \(n = 4\).

The formula for the amount at the end of year 4 can also be expressed in terms of the amount at the end of year 3:

\(A_4 = A_3 (1 + r)\)

Substitute the given values:

\(73,205 = 66,550 (1 + r)\)

We solve for \(r\):

\(1 + r = \frac{73,205}{66,550}\)

Calculate:

\(1 + r = 1.1\)

Thus, \(r = 1.1 - 1 = 0.1\) or 10%.

The rate percent per annum is 10%. Therefore, the correct answer is \(0.1\) or \(10\%\).