In what time period will ` 3750 amount to ` 6480 at 20% per annum compoundedannually?

To solve this problem, we will use the formula for compound interest which 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 = 6480 P = 3750 r = 20% per annum = 0.20 n = 1 (since it is compounded annually)

We need to find t.

Substituting the given values into the formula, we get:

6480 = 3750 (1 + 0.20/1)^(1*t)

Solving the equation for t:

First, divide both sides by 3750:

6480/3750 = (1 + 0.20)^t

1.728 = 1.2^t

Taking the natural logarithm (ln) of both sides:

ln(1.728) = t * ln(1.2)

Now, divide both sides by ln(1.2) to solve for t:

t = ln(1.728) / ln(1.2)

Using a calculator to find the natural logarithms and perform the division, we get:

t ≈ 3.6 years

So, it will take approximately 3.6 years for 3750 to amount to 6480 at an annual interest rate of 20% compounded annually.