The amount that must be investigated at 6%p.a. compounding annually to have K4500 at the end of 5years is ?

To find the amount that must be invested at 6% p.a. compounding annually to have K4500 at the end of 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

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

In this case, we want to find the principal amount (P) that must be invested to have K4500 at the end of 5 years. We know that:
A = K4500
r = 6% = 0.06
n = 1 (compounded annually)
t = 5 years

Plugging these values into the formula, we get:
K4500 = P(1 + 0.06/1)^(1*5)
K4500 = P(1.06)^5
K4500 = P(1.338225)

Now, we can solve for P:
P = K4500 / 1.338225
P = K3358.85

Therefore, the amount that must be invested at 6% p.a. compounding annually to have K4500 at the end of 5 years is K3358.85.

The formula for compound interest is:

$$ A = P(1 + r)^t $$

Where:

- A = the future value of the investment/loan, including interest
- P = the principal investment/loan amount
- r = the annual rate of interest in decimal form
- t = the number of years the money is invested or borrowed for

In this question, we are given the following information:

- A = K4500
- r = 6% p.a. = 0.06
- t = 5 years

We want to find the value of P, the principal investment.

Substituting the given values into the formula, we get:

$$ 4500 = P(1 + 0.06)^5 $$

$$ 4500 = P(1.06)^5 $$

$$ 4500 = P(1.33823) $$

Dividing both sides by 1.33823, we get:

$$ P = \frac{4500}{1.33823} $$

$$ P = K3360.49 $$

Therefore, the amount that must be investigated at 6%p.a. compounding annually to have K4500 at the end of 5years is K3360.49.