debt of RM3,000 on 8 February 2018 became RM3,150 on 8 June 2018. Calculate the value of the debt on 19 May 2018 using the Banker's Rule. (hint: find r% first)
To calculate the value of the debt on 19 May 2018 using the Banker's Rule, we need to first find the r% (annual interest rate).
Using the Banker's Rule formula:
(Value after x days / Value before x days) = (1 + r%)^(x/365)
We have the following information:
Value before x days = RM3,000
Value after x days = RM3,150
x = 120 days (8 June 2018 - 8 February 2018)
Plugging in the values into the formula:
(3,150 / 3,000) = (1 + r%)^(120/365)
Simplifying and solving for (1 + r%):
1 + r% = (3,150 / 3,000)^(365/120)
1 + r% = (1.05)^(3.0417)
1 + r% = 1.15712
Subtracting 1 from both sides:
r% = 0.15712
To convert r% to a decimal, divide by 100:
r = 0.0015712
Now, let's calculate the value of the debt on 19 May 2018 (100 days from 8 February 2018).
Using the Banker's Rule formula:
Value after x days = Value before x days * (1 + r%)^(x/365)
Value after 100 days = RM3,000 * (1 + 0.0015712)^(100/365)
Value after 100 days = RM3,000 * (1.0015712)^(0.27397)
Value after 100 days = RM3,082.62 (rounded to 2 decimal places)
Therefore, the value of the debt on 19 May 2018 is approximately RM3,082.62.