bernard burrows rm8889 at 15%per annum simple interest. he agrees to settle the loan by paying x ringgit, 2x ringgit and 3x ringgit in two months, five months and nine months respectively.find the value of x using the present as the focal date
8889=x(1+0.15*0.16)^_1+2x(1+0.15*0.416)^_1+3x(1+0.15*0.75) this is my solution.thank you for your time.
To find the value of x in this problem, we can use the formula for simple interest:
Simple Interest = Principal * Rate * Time
In this case, Bernard borrowed RM8889 at a rate of 15% per annum. Let's calculate the interest for each payment and then set up the equation.
First payment (2 months):
Simple interest = x * 0.15 * (2/12)
Amount to be paid = Principal + Simple interest
Amount to be paid = 8889 + x * 0.15 * (2/12)
Amount to be paid = 8889 + 0.025 * x
Second payment (5 months):
Simple interest = 2x * 0.15 * (5/12)
Amount to be paid = Principal + Simple interest
Amount to be paid = 8889 + 2x * 0.15 * (5/12)
Amount to be paid = 8889 + 0.125 * x
Third payment (9 months):
Simple interest = 3x * 0.15 * (9/12)
Amount to be paid = Principal + Simple interest
Amount to be paid = 8889 + 3x * 0.15 * (9/12)
Amount to be paid = 8889 + 0.3375 * x
Now let's set up the equation using the present as the focal date:
8889 + 0.025 * x = Amount to be paid in two months
8889 + 0.125 * x = Amount to be paid in five months
8889 + 0.3375 * x = Amount to be paid in nine months
Now, we can substitute the values into the equation:
8889 + 0.025 * x = x
8889 + 0.125 * x = 2x
8889 + 0.3375 * x = 3x
Simplifying these equations:
0.975 * x = 8889
1.875 * x = 8889
2.6625 * x = 8889
Solving these equations, we can find the value of x:
x = 8889 / 0.975
x = 8889 / 1.875
x = 8889 / 2.6625
x = 9118.46
x = 4741.60
x = 3340.38
Therefore, the value of x is approximately RM9118.46, RM4741.60, or RM3340.38, depending on which equation we use.