RM X was deposited in a savings account at 4.0% interest compounded monthly. Forty later, RM 4,200 was withdrawn from the account and the balance was RM 4,212.39. Find the value of X.
P = Po(1+r)^n.
r = 0.04/12 = 0.0033 = monthly % rate.
n = 40 compounding periods.
P = X(1+0.00333)^40 = 4200+4212.39
1.1422x = 8412.39
X = 7364.91
Well, isn't this a mathematical circus! Let's get cracking, shall we?
First, let's break down the problem. We have an initial deposit, which we'll call X, that grows at 4% interest compounded monthly. After some time, a withdrawal of RM 4,200 is made, and the remaining balance is RM 4,212.39.
Now, let's put our clown noses on and start solving. The formula we'll need here is the future value of an investment, which is given by:
A = P(1 + r/n)^(nt)
Where:
A is the final balance (RM 4,212.39),
P is the initial deposit (X),
r is the annual interest rate (4.0% or 0.04),
n is the number of times interest is compounded in a year (12, since it's compounded monthly), and
t is the number of years (40, since the withdrawal happens after 40 years).
Now, let's plug in the values and solve for X:
4,212.39 = X(1 + 0.04/12)^(12*40)
Now, let's put our math clown hats on and solve!
4,212.39 = X(1.0033333)^480
And now for the grand finale:
X = 4,212.39 / (1.0033333)^480
Calculating that, we find that X is approximately RM 259.84!
And that's the value of X, folks! Remember, even math can be entertaining when you add some clownish charm to it.
To find the value of X, we need to work backward from the given information.
Step 1: Let's assume that the initial deposit is X in the savings account.
Step 2: The interest rate is 4.0% compounded monthly. To convert it to a monthly interest rate, we divide 4.0% by 100:
Monthly Interest Rate = 4.0% / 100 = 0.04
Step 3: We know that after 40 months, RM 4,200 was withdrawn from the account and the remaining balance was RM 4,212.39.
Step 4: To find the future value after 40 months, we will use the formula for compound interest:
Future Value = Principal * (1 + Monthly Interest Rate)^Number of Months
Substituting the given values:
4,212.39 = X * (1 + 0.04)^40
Step 5: Next, we will divide both sides of the equation by (1 + 0.04)^40:
4,212.39 / (1 + 0.04)^40 = X
Calculating this, we find:
X ≈ 2401.00
The value of X is approximately RM 2,401.00.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Here, A represents the final balance, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the time in years.
In this case, the initial balance after forty years is unknown (we'll call it X), the final balance is RM 4,212.39, the annual interest rate is 4.0% (or 0.04 as a decimal), and the interest is compounded monthly (so n = 12).
We can rearrange the formula to solve for X:
X = A / (1 + r/n)^(nt)
Substituting the known values:
X = RM 4,212.39 / (1 + 0.04/12)^(12*40)
Now we can solve this equation to find the value of X.