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)

Answer 1

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.