TWO YEARS AGO, KIM INVESTED RMP AT HER ACCOUNT WHICH EARNS r% simple interest . after eighteen months , she noticed that the amount had become rm 10450 and today amount is rm 10600 . FIND THE VALUE OF p and r

r% should be 3%

n P should be RM10,000

To find the value of p and r, we can set up two equations based on the information given.

Let's start by finding the value of p:

1. Using the formula for simple interest: Interest = (Principal * Rate * Time) / 100
After 18 months, the interest earned is RM 10450 - P.
So, the equation becomes: (P * R * 18) / 100 = 10450 - P

Now, let's find the value of r:

2. Since the account balance after 2 years is RM 10600, we can use the formula for compound interest to calculate the final amount:
Final Amount = P * (1 + (R/100))^2
10600 = P * (1 + (R/100))^2

Now, we have two equations:

Equation 1: (P * R * 18) / 100 = 10450 - P
Equation 2: 10600 = P * (1 + (R/100))^2

We can solve these equations simultaneously to find the values of p and r.

To find the values of p and r, we need to break down the problem into two parts. First, we'll find the value of p, and then we'll find the value of r.

Let's start by finding the value of p.

We know that after 18 months, the amount had become RM 10,450. Since the interest is calculated using simple interest, we can use the formula:

A = P(1 + rt)

Where:
A = Final amount
P = Principal amount
r = Interest rate (as a decimal)
t = Time (in years)

From the given information, we know:
A = RM 10,450
t = 18 months, which is equal to 18/12 = 1.5 years
We need to find P.

Substituting the values into the formula, we get:

10,450 = P(1 + r * 1.5)

Next, let's find the value of r.

We know that the current amount is RM 10,600. Using the same formula, we have:

10,600 = P(1 + r * 2)

Now we have two equations:

Equation 1: 10,450 = P(1 + 1.5r)
Equation 2: 10,600 = P(1 + 2r)

To solve these equations simultaneously, we can use a common method like substitution or elimination.

Let's use the substitution method. Rearrange equation 1 to get P in terms of r:

P = 10,450 / (1 + 1.5r)

Now substitute this value of P into equation 2:

10,600 = (10,450 / (1 + 1.5r)) * (1 + 2r)

Simplify the equation and solve for r. This will give us the value of r. Once we have r, substitute it back into the equation to find the value of p.

Please note that due to large calculations involved in solving these equations, it is advisable to use a calculator or an algebraic software to find the value of p and r accurately.

P(1+r)^18 = 10450

P(1+r)^24 = 10600

(1+r)^6 = 10600/10450
r = 0.0023782
Now find P.

Note that r is the monthly interest. Adjust to get the annual rate.