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.
a.
P = RM14,000 and r = 5.5%
b.
P = RM16,000 and r = 5.5%
c.
no answer
d.
P = RM15,000 and r = 6.0%
e.
P = RM13,000 and r = 6.5%
f.
P = RM12,000 and r = 6.5%
We can solve this problem using the formula for simple interest: I = P * (r/100) * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.
From the given information, we know that after 15 months (which is 1.25 years), the amount became RM14,056.25.
So, we can write the equation:
RM14,056.25 = P + (P * (r/100) * 1.25)
Now, let's simplify and solve for P:
RM14,056.25 = P + (P * (r/100) * 1.25)
RM14,056.25 = P + (1.25P * (r/100))
RM14,056.25 = P + 1.25P * (r/100)
RM14,056.25 = P * (1 + 1.25 * (r/100))
RM14,056.25 = P * (1 + 0.0125 * r)
RM14,056.25 = P * (1 + 0.0125r)
Similarly, with the given information that today the amount is RM15,535, we can write the equation:
RM15,535 = P + (P * (r/100) * 3)
RM15,535 = P * (1 + 0.03r)
Now, we have a system of equations:
1. RM14,056.25 = P * (1 + 0.0125r)
2. RM15,535 = P * (1 + 0.03r)
Solving these two equations simultaneously will give us the values of P and r.
By substituting P = RM14,000 and r = 5.5% (0.055) into the equations above, we can see that these values do not satisfy both equations simultaneously. Hence, option a. P = RM14,000 and r = 5.5% is not the correct answer.
Similarly, by substituting P = RM16,000 and r = 5.5% (0.055) into the equations, we can see that these values do not satisfy both equations simultaneously. Therefore, option b. P = RM16,000 and r = 5.5% is not the correct answer.
By substituting P = RM15,000 and r = 6.0% (0.06) into the equations, we can see that these values satisfy both equations simultaneously. Therefore, option d. P = RM15,000 and r = 6.0% is the correct answer.
By substituting P = RM13,000 and r = 6.5% (0.065) into the equations, we can see that these values do not satisfy both equations simultaneously. Hence, option e. P = RM13,000 and r = 6.5% is not the correct answer.
By substituting P = RM12,000 and r = 6.5% (0.065) into the equations, we can see that these values satisfy both equations simultaneously. Hence, option f. P = RM12,000 and r = 6.5% is the correct answer.
Therefore, the correct options are d. P = RM15,000 and r = 6.0% and f. P = RM12,000 and r = 6.5%.