Math, asked by bankofficer94, 2 months ago

The compound interest earned on a certain sum for
the first two years and the first three years were
6,600 and 10,920 respectively when ccmpounded
annually. What is the rate of interest?
(1) 15% p.a.
(2) 20% p.a. (3) 25% p.a.
(4) 30% p.a. (5) None of these

Answers

Answered by Afreenakbar

Answer:

The correct answer is (5) None of these.

Step-by-step explanation:

We can use the compound interest formula to determine the rate of interest:

$A = P(1 + \frac{r}{n})^{nt}$

Where:

A = Total amount including interest

P = Principal amount (initial sum)

r = Rate of interest (in decimal form)

n = Number of times interest is compounded per year

t = Number of years

Let's calculate the interest rate using the information provided:

For First two years:

$6,600 = P(1 + \frac{ r}{1})^{(1 \times 2)}$

6,600 = P(1 + r)² ... (Equation 1)

For the first three years:

$10,920 = P(1 + \frac{r}{1})^{(1 \times 3)}$

10,920 = P(1 + r)³ ... (Equation 2)

Dividing Equation 2 by Equation 1:

$\frac{10,920}{6,600} = \frac{ P(1 + r)^3}{P(1 + r)^2}$

1.6545 = (1 + r)

Solving for r:

1 + r = 1.6545

r = 1.6545 - 1

r = 0.6545

The interest rate is roughly 0.6545 percent, or 65.45%.

None of the available alternatives exactly match the determined interest rate. Therefore, the correct answer is (5) None of these.