eighteen months ago, a sum money of money was invested. Now the investment is worth RM 10 900. If the investment is extended for another 20 months, it will become RM 11 900. Find the original and simple interest rate that was offered
P(1+18*r/1200) = 10900
P(20*r/1200) = 100
Now finish it off
To solve this problem, we need to find the original amount invested and the simple interest rate.
Let's assume the original amount invested is P (in RM).
After 18 months, the investment is worth RM 10,900, which means the interest earned over 18 months is RM 10,900 - P.
We can calculate the simple interest rate using the formula:
Simple Interest = (Principal Amount * Interest Rate * Time) / 100
So, after 18 months:
10,900 - P = (P * R * 18) / 100 -- (equation 1)
After another 20 months (total 38 months), the investment becomes RM 11,900. So, the interest earned over 38 months is RM 11,900 - P.
Using the same formula, we get:
11,900 - P = (P * R * 38) / 100 -- (equation 2)
Now, we have two equations with two unknowns.
We can solve these equations simultaneously to find the values of P (original amount) and R (interest rate).
Let's solve these equations:
From equation 1:
10,900 - P = (P * R * 18) / 100
=> 1,090,000 - 100P = 18PR
From equation 2:
11,900 - P = (P * R * 38) / 100
=> 1,190,000 - 100P = 38PR
We can solve these equations simultaneously by subtracting equation 1 from equation 2:
(1,190,000 - 1,090,000) - (38PR - 18PR) = 18PR - 18PR
=> 100,000 = 20PR
=> PR = 5,000
Substituting PR = 5,000 into equation 1:
1,090,000 - 100P = 18PR
=> 1,090,000 - 100P = 18(5,000)
=> 1,090,000 - 100P = 90,000
=> 100P = 1,000,000
=> P = 10,000
Therefore, the original amount invested was RM 10,000, and the interest rate offered was 5%.
To find the original investment and the simple interest rate that was offered, we can use the formula for simple interest:
Simple Interest (SI) = Principal amount (P) x Interest Rate (R) x Time period (T)
Given that the investment was worth RM 10,900 after 18 months and RM 11,900 after 20 months, we can set up two equations:
1) 10,900 = P + (P x R x 18/12) -> Equation 1 (using the value after 18 months)
2) 11,900 = P + (P x R x 20/12) -> Equation 2 (using the value after 20 months)
To solve these equations, we can use the substitution method. Rearrange Equation 1 to solve for P:
10,900 = P + (P x R x 18/12)
10,900 = P(1 + (R x 18/12))
10,900 = P(1 + 1.5R) -> Equation 3
Similarly, rearrange Equation 2 to solve for P:
11,900 = P + (P x R x 20/12)
11,900 = P(1 + (R x 20/12))
11,900 = P(1 + (5R/3))
11,900 = P(3 + 5R)/3 -> Equation 4
Now, we can substitute Equation 3 into Equation 4:
10,900(3 + 5R)/3 = P(1 + 1.5R)
Next, we can cross multiply and simplify:
32,700 + 54,500R = 3P + 4.5PR
32,700 + 54,500R = 3P(1 + 1.5R)
Now, let's solve for P:
3P(1 + 1.5R) - 54,500R = 32,700
Expand and rearrange the terms:
3P + 4.5PR - 54,500R = 32,700
3P + 4.5PR = 54,500R + 32,700
3P(1 + 1.5R) = 54,500R + 32,700
3P = (54,500R + 32,700) / (1 + 1.5R)
Finally, plug in different interest rate values (R) and calculate the corresponding principal amount (P). The interest rate that yields a principal amount closest to a whole number is the estimated simple interest rate offered.
Note: Alternatively, you may use numerical computation methods such as using a graphing calculator or a spreadsheet program to solve this equation for different values of R to find the closest estimate.