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 on 13 august 1993, rm600 was withdrawn and the balance as on 31 december 1993 was RM 8900.calculate the value of X using exact time and 360 day year.
I'll just guess at the numbers of days involved. You can find out exactly and adjust the expression.
(x(1+.10/360)^20 - 600)(1+.10/360)^108 = 8900
x = 9185.83
RM8,900 = [ X (1+0.1/360)^19 - RM600](1+0.1/360)^140
RM8,900/(1+0.1/360)^140 = X (1+0.1/360)^19 - RM600
RM8560.58 + RM600 = X (1+0.1/360)^19
RM9160.58 = X (1+0.1/360)^19
RM9160.58/(1+0.1/360)^19 = X
RM9112.36 = X
Therefore, X is RM9112.36#
To find the value of X, we need to calculate the future value of the initial deposit after accounting for the withdrawal and compounding interest.
First, let's calculate the number of days between 25 July 1993 and 13 August 1993.
Days from 25 July 1993 to 13 August 1993:
= 13 August 1993 - 25 July 1993
= 19 days
Next, let's calculate the number of days between 13 August 1993 and 31 December 1993.
Days from 13 August 1993 to 31 December 1993:
= 31 December 1993 - 13 August 1993
= 141 days
Now, let's calculate the future value of the initial deposit after accounting for the withdrawal and the compounded interest.
Future Value = Initial Deposit + Interest - Withdrawal
First, let's calculate the interest:
Interest = Initial Deposit * (1 + (Interest Rate / Number of Days in a Year))^(Number of Days from 25 July 1993 to 13 August 1993)
Interest = X * (1 + (10% / 360))^(19)
Now, let's calculate the future value:
Future Value = X + Interest - RM600
Future Value = X + X * (1 + (10% / 360))^(19) - RM600
Finally, let's calculate the value of X using the balance on 31 December 1993:
RM8900 = X + X * (1 + (10% / 360))^(19) - RM600
Now, we can solve this equation to find the value of X.
To calculate the value of X in this scenario, we can use the formula for compound interest:
\[A = P \left(1 + \frac{r}{n}\right)^{nt}\]
Where:
A is the final amount in the savings account (RM 8900),
P is the initial amount (X) we want to find,
r is the annual interest rate (10%),
n is the number of times the interest is compounded per year (365 in this case since it is compounded daily),
t is the time in years (expressed in terms of a fraction of a year).
To solve for X, we need to determine the time (t) between July 25 and August 13, and the time between August 13 and December 31.
First, let's find the time from July 25 to August 13:
There are 365 days in a year, so the time is \(\frac{{19}}{{365}}\).
Next, let's find the time from August 13 to December 31:
Again, there are 365 days in a year, so the time is \(\frac{{139}}{{365}}\).
Now, we can calculate X:
\[8900 = X \left(1 + \frac{{10\%}}{{365}}\right)^{365 \cdot \frac{{19}}{{365}}} - 600 \left(1 + \frac{{10\%}}{{365}}\right)^{365 \cdot \left(\frac{{19}}{{365}} + \frac{{139}}{{365}}\right)}\]
Simplifying this equation will give us the value of X.