Two years ago, Kim Ean invested RM P in her account which earns r% simple interest. After 18 months, she noticed that the amount had become RM 10,450 and today, the amount is RM 10,600. Find the value of r.
Since the interest appears to be applied monthly, use 1/12 the annual rate. After n months,
A = P(1 + n*r/12100)
Now use the given data
P(1+18r/1200) = 10450
P(1+24r/1200) = 10600
Dividing #2 by #1, we have
(1+24r/1200)/(1+18r/1200) = 10600/10450
r = 3%
Two years ago, Khaled invested RM P in his account which earns r% simple interest.
After eighteen months, he noticed that the amount had become RM10450 and today the
amount is RM 10600. Find the value of P and r.
Well, Kim Ean seems to be quite the clairvoyant investor! She can predict the future value of her account better than I can predict punchlines! Nevertheless, let's solve this mathematical mystery.
If the amount increased from RM 10,450 to RM 10,600 in 18 months, we can calculate the interest earned during that time. The interest earned is RM 10,600 - RM 10,450 = RM 150.
Now, let's go back in time to 18 months ago, when the account had RM P. Kim Ean earned interest of RM 150 over those 18 months.
Since simple interest is calculated based on the principal amount (RM P) and the interest rate (r), we can use the formula:
Interest = Principal × Rate × Time
Substituting the given values, we have:
RM 150 = RM P × r × 18/12
Simplifying this, we get:
150 = P × r × 3/2
Dividing both sides by 3/2, we find:
150 ÷ 3/2 = P × r
Doing the math:
150 × 2/3 = P × r
100 = P × r
To find the value of r, we divide both sides of the equation by P:
r = 100 / P
So, the value of r, in terms of P, is r = 100 / P.
Now, all we need is the initial principal amount, P, to get the value of r. Unfortunately, the information you provided does not include the value of P. Without P, poor r will remain a mystery, much like why clowns wear such big shoes!
To find the value of r, we can use the formula for simple interest:
Simple Interest = Principal x Rate x Time
Let's break down the given information and solve step by step.
1. Two years ago, Kim Ean invested RM P in her account, which earns r% simple interest. Let's consider the principal amount as P.
2. After 18 months (or 1.5 years), she noticed that the amount had become RM 10,450. This amount includes the principal and the interest earned over 1.5 years.
3. Today, the amount is RM 10,600. This represents the total amount after two years, including both the principal and the interest earned.
To find the value of r, we need to calculate the interest earned in 1.5 years and then determine the rate.
Step 1: Calculate the interest earned in 1.5 years.
Interest = Total amount after 1.5 years - Principal
Interest = RM 10,450 - P
Step 2: Calculate the interest earned in 2 years.
Total interest earned in 2 years = Total amount today - Principal
Total interest earned in 2 years = RM 10,600 - P
Since the simple interest formula is:
Simple Interest = Principal x Rate x Time
Step 3: Set up the equation using the two interest values and solve for r.
(RM 10,450 - P) = P x (r/100) x (1.5 years)
(RM 10,600 - P) = P x (r/100) x (2 years)
Step 4: Equate the two expressions for interest and solve for r.
(RM 10,450 - P) = P x (r/100) x (1.5 years)
(RM 10,600 - P) = P x (r/100) x (2 years)
Now, you can solve these two equations simultaneously to find the value of r. Use algebraic manipulation to isolate r and then solve for its value.