A 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 find the value of the debt on 19 May 2018 using the Banker's Rule, we need to calculate the value of r%.
The Banker's Rule formula is:
Value after time = Value before time * (1 + r%)^(number of days / 365)
Let's denote the value of the debt on 19 May 2018 as X. We know the following:
Debt on 8 February 2018 = RM3,000
Debt on 8 June 2018 = RM3,150
Using the Banker's Rule formula, we can set up the following equation:
RM3,150 = RM3,000 * (1 + r%)^(120 / 365)
Now we can solve for r%.
Divide both sides of the equation by RM3,000:
RM3,150 / RM3,000 = (1 + r%)^(120 / 365)
1.05 = (1 + r%)^(120 / 365)
Take the logarithm of both sides of the equation to solve for r%:
log(1.05) = log((1 + r%)^(120 / 365))
Using the property log(a^b) = b * log(a):
log(1.05) = (120 / 365) * log(1 + r%)
Now we can solve for log(1 + r%):
(120 / 365) * log(1 + r%) = log(1.05)
Divide both sides of the equation by (120 / 365):
log(1 + r%) = log(1.05) / (120 / 365)
Calculate log(1 + r%):
log(1 + r%) ≈ 0.0487
Now, we can find the value of r% by converting log(1 + r%) back to the exponential form:
1 + r% = 10^(0.0487)
1 + r% ≈ 1.1194
Subtract 1 from both sides of the equation:
r% ≈ 1.1194 - 1
r% ≈ 0.1194
The value of r% is approximately 0.1194, or 11.94%.
Now we can find the value of the debt on 19 May 2018:
X = RM3,000 * (1 + 0.1194)^(100 / 365)
X ≈ RM3,031.05
Therefore, the value of the debt on 19 May 2018 using the Banker's Rule is approximately RM3,031.05.