The formula for compound interest is A = P(1 + r/n)^(nt), where:

A = the amount of money accumulated after n years, including interest.
P = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times that interest is compounded per year
t = time the money is invested for in years

Given in the problem:
A = Rs.3362
P = Rs.3200
r = 10% per annum = 0.10 (in decimal)
n = compounded quarterly = 4 times a year

We need to find t.

Substituting the given values in the formula, we get:

3362 = 3200(1 + 0.10/4)^(4t)

Solving the equation for t:

(3362/3200) = (1 + 0.10/4)^(4t)

1.050625 = (1.025)^(4t)

Taking the natural log (ln) on both sides:

ln(1.050625) = 4t * ln(1.025)

Solving for t:

t = ln(1.050625) / (4 * ln(1.025))

t ≈ 0.5 years

So, the closest option is 1 year.

Question

The formula for compound interest is A = P(1 + r/n)^(nt), where:

A = the amount of money accumulated after n years, including interest.
P = principal amount (the initial amount of money)
r = annual interest rate (in decimal)
n = number of times that interest is compounded per year
t = time the money is invested for in years

Given in the problem:
A = Rs.3362
P = Rs.3200
r = 10% per annum = 0.10 (in decimal)
n = compounded quarterly = 4 times a year

We need to find t.

Substituting the given values in the formula, we get:

3362 = 3200(1 + 0.10/4)^(4t)

Solving the equation for t:

(3362/3200) = (1 + 0.10/4)^(4t)

1.050625 = (1.025)^(4t)

Taking the natural log (ln) on both sides:

ln(1.050625) = 4t * ln(1.025)

Solving for t:

t = ln(1.050625) / (4 * ln(1.025))

t ≈ 0.5 years

So, the closest option is 1 year.

Knowee AI · Accepted Answer