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 on 13 august 1993, rm600 was withdrawn and the balance as on 31 december 1993 was RM 8900.calculate the value of X using exact time and 360 day year.
(1+.10/360)^20 - 600)(1+.10/360)^108 = 8900
x = 9185.83
but the answer is 9112.37
What you wanted as an equation is ...
[ x( 1 + .1/360)^20 - 600 ](1+.1/360)^108 = 8900
x(1+.1/360)^20(1+.1/360)^108 - 600(1+.1/360)^108 = 8900
x((1.00557024)((1.03045024) - 618.2701442 = 8900
x(1.036190095 = 9518.270144
x = 9185.83
ooooohhh thanks
how to get the 20 and 108
This is the way how we can calculate it.
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 solve this problem, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Initial deposit (unknown in this case)
r = Annual interest rate (10% in this case)
n = Number of times interest is compounded per year (daily in this case)
t = Time in years
First, we need to determine the number of days between July 25 and August 13, 1993:
Number of days = August 13 - July 25 + 1 = 20
We can then calculate the amount remaining after the withdrawal on August 13, 1993:
A = P(1 + (0.10/360))^20 - 600
Next, we need to calculate the number of days between August 13 and December 31, 1993:
Number of days = December 31 - August 13 = 140
Finally, we can calculate the value of X by equating the remaining balance to RM 8900:
8900 = P(1 + (0.10/360))^20 * (1 + (0.10/360))^140
Simplifying the equation further:
(1 + (0.10/360))^160 = 8900/P
Taking the 160th root of both sides:
1 + (0.10/360) = (8900/P)^(1/160)
Solving for P:
P = 8900 / (1 + (0.10/360))^(1/160)
Using a calculator or any programming language, we can evaluate this expression to find that P ≈ 9112.37.
Therefore, the value of X (the initial deposit) is approximately RM 9112.37.