Munshi saved rm 500 a year ago and x ringgit today , in an account that pays 8.5% compounded semi- annually . Find the value of x if he wants rm 1000 in the account one year from today.
He gets 2 years of interest on the original 500, and 1 year on the extra x. So, we want
500(1 + .085/2)^(2*2) + x(1 + .085/2)^(2*1) = 1000
485.98
Abi wishes to invest RM8,000 in a fixed deposit account for one year. He has two options:
AAA Bank which offers 3.7% interest compounded semi-annually.
BBB Bank which offers 3.75% interest compounded annually.
To find the value of x, we need to calculate the future value of Munshi's savings after one year. We can use the formula for compound interest:
Future Value = Principal × (1 + Interest Rate/Number of Compounding Periods)^(Number of Compounding Periods × Time)
Let's break down the information given:
Principal (initial amount saved a year ago) = RM 500
Interest Rate = 8.5% (or 0.085, as a decimal)
Number of Compounding Periods = 2 (since interest is compounded semi-annually)
Time = 1 year
Now we can plug these values into the formula to find the future value:
Future Value = 500 × (1 + 0.085/2)^(2 × 1)
Future Value = 500 × (1 + 0.0425)^2
Future Value = 500 × (1.0425)^2
Future Value = 500 × 1.08600625
Future Value = 543.003125
So, after one year, Munshi's savings (including the initial RM 500 and x) will grow to RM 543.003125.
Now, we need to determine the value of x that will make the total amount in the account reach RM 1000 after one year. We can set up the equation:
Total Amount = x + 543.003125
Since we want the total amount to be RM 1000 after one year, we can write:
1000 = x + 543.003125
Now, we can solve for x:
x = 1000 - 543.003125
x = 456.996875
Therefore, Munshi should have RM 456.996875 (rounded to 2 decimal places) today in order to have RM 1000 in the account one year from today.