A sum of money,X was deposited in a saving account at 10 percent compounded daily on 25 july 1993. on 13 august 1993, rm600 was withdrawn and the balance as on 31 december 1993 was RM 8900.calculate the value of X using exact time and 360 day year.
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All that was required of you want a bit of "counting" .
To calculate the value of X, we need to break down the problem into different time periods and use the compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (in decimal)
n = number of times the interest is compounded per year
t = time in years
In this case, we have the interest rate compounded daily, so n equals 365 (the number of days in a year) for exact time calculations and t will be the number of days.
Let's determine the value of X using this formula:
Step 1: Calculate the number of days from July 25th to August 13th.
Number of days = 13 - 25 = -12 (Since we move back in months, we have a negative value.)
Step 2: Calculate the interest accrued from July 25th to August 13th.
Interest accrued = RM 600
Step 3: Calculate the number of days from August 13th to December 31st.
Number of days = 31 + 30 + 31 = 92
Step 4: Calculate the number of days from July 25th to December 31st.
Number of days = 365 - 12 + 92 = 445
Step 5: Calculate the final amount on December 31st using the formula.
RM 8900 = X(1 + 0.1/365)^(365*445)
Now, we can solve this equation to find the value of X.
Dividing both sides of the equation by (1 + 0.1/365)^(365*445), we get:
RM 8900 / (1 + 0.1/365)^(365*445) = X
Using a calculator, compute the right side of the equation and solve for X to determine the initial deposit amount.