3 years ago, Aisyah invested RM P in her account which earns r% simple interest. After 15 months, she noticed that the amount had become RM14,056.25 and today the amount is become RM15,535. Find the value of P and r.
Let's solve this step by step:
Step 1: Find the value of P
Given that Aisyah noticed the amount became RM14,056.25 after 15 months, we can use the formula for simple interest:
Simple Interest = Principal × Rate × Time
We know that:
Simple Interest = RM14,056.25
Principal = P
Rate = r (as a decimal)
Time = 15 months
So we have the equation:
RM14,056.25 = P × r × (15/12)
Simplifying, we get:
RM14,056.25 = P × r × 1.25
Step 2: Find the value of r
Now let's find the rate r. We are given that today (after 3 years), the amount has become RM15,535. Using the same formula:
RM15,535 = P × r × 3
Step 3: Solve the system of equations
Now we have a system of two equations with two variables:
RM14,056.25 = P × r × 1.25 ----(1)
RM15,535 = P × r × 3 ----(2)
To solve this system, divide equation (2) by equation (1):
(RM15,535) / (RM14,056.25) = (P × r × 3) / (P × r × 1.25)
Simplifying, we get:
1.1067792 ≈ 2.4
Therefore, we can conclude that P × r = 1.1067792.
Step 4: Solve for P and r
We know P × r = 1.1067792. Let's solve for P by isolating P on one side:
P × r = 1.1067792
P = 1.1067792 / r
Now substitute this into equation (1) to solve for r:
RM14,056.25 = (1.1067792 / r) × r × 1.25
Simplifying, we get:
RM14,056.25 = 1.384724 × r
Divide both sides by 1.384724:
r = RM14,056.25 / 1.384724
r ≈ 10,140.91
Now substitute the value of r back into the equation P × r = 1.1067792 to solve for P:
P × 10,140.91 = 1.1067792
P = 1.1067792 / 10,140.91
P ≈ 0.000109
Therefore, the value of P is approximately RM0.000109 and the value of r is approximately 10,140.91%.