2. Four years ago, Remy deposited RMX in a savings account that paid interest at 6.5% compounded
monthly. Today, another RM2,000 is deposited into the same account. If the accumulated amount
in the account three years from now is RM11500, find the value of X.
First, we need to calculate the accumulated amount of RMX after four years:
A = P(1 + r/n)^(nt)
Where:
A = accumulated amount
P = principal amount (initial deposit)
r = annual interest rate (6.5% or 0.065)
n = number of times interest is compounded per year (12 for monthly)
t = number of years (4)
So, for RMX after four years:
A = RMX(1 + 0.065/12)^(12*4)
A = RMX(1 + 0.00541667)^48
A = RMX(1.00541667)^48
A = 1.28290707RMX
Next, we add the RM2,000 deposited today to get the total accumulated amount after the next three years:
Total Accumulated Amount = 1.28290707RMX + 2,000
Given that the accumulated amount after 3 more years is RM11,500, we have:
1.28290707RMX + 2,000 = 11,500
Solving for RMX:
1.28290707RMX = 9,500
RMX = 9,500 / 1.28290707
RMX = 7,399.17
Therefore, the value of X is 7,399.17.