General mathematics

Question

Win Metawin’s debt of Php 50, 000 with interest of 18% compounded

quarterly will be discharged, interest included, by payments of Php 7, 000 at the

end of every three months for as long as necessary. Find

1. The outstanding principal just after the 2nd payment;

2. The outstanding principal just after the 7th payment; and

3. The outstanding balance just after the regular pay

Answer 1

To solve this problem, we'll use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = the final amount including interest P = the principal amount (initial debt) r = the annual interest rate (18% = 0.18) n = the number of compounding periods per year (quarterly = 4) t = the number of years

Let's calculate the outstanding principal just after the 2nd payment:

Step 1: Calculate the quarterly interest rate Quarterly interest rate = annual interest rate / number of compounding periods per year Quarterly interest rate = 0.18 / 4 = 0.045

Step 2: Calculate the outstanding principal after the 2nd payment Principal after the 1st payment = P - payment amount Principal after the 1st payment = 50000 - 7000 = 43000

Outstanding principal after the 2nd payment = Principal after the 1st payment * (1 + quarterly interest rate)^(n * t) Outstanding principal after the 2nd payment = 43000 * (1 + 0.045)^(4 * 1) Outstanding principal after the 2nd payment = 43000 * (1.045)^4 Outstanding principal after the 2nd payment ≈ 43000 * 1.191012025 = 51258.52 ≈ Php 51,258.52

Now let's calculate the outstanding principal just after the 7th payment:

Outstanding principal after the 7th payment = Principal after the 2nd payment * (1 + quarterly interest rate)^(n * t) Outstanding principal after the 7th payment = 51258.52 * (1 + 0.045)^(4 * 5) Outstanding principal after the 7th payment ≈ 51258.52 * (1.045)^20 = 60626.44 ≈ Php 60,626.44

Finally, let's calculate the outstanding balance just after the regular payment:

Outstanding balance just after the regular payment = Outstanding principal after the 7th payment - payment amount Outstanding balance just after the regular payment = 60626.44 - 7000 = 53626.44 ≈ Php 53,626.44

So the answers to the given questions are:

1. The outstanding principal just after the 2nd payment is approximately Php 51,258.52.
2. The outstanding principal just after the 7th payment is approximately Php 60,626.44.
3. The outstanding balance just after the regular payment is approximately Php 53,626.44.