John has a personal loan of k4800 and is being charged 8.85% interest compounded monthly. He has decided to pay back k1000 every 6 months. How much will he owe straight after his first payment
To calculate how much John will owe straight after his first payment, we need to first determine the interest accrued on his initial loan amount.
First, let's calculate the interest accrued after 6 months:
Interest for the first 6 months = Principal * (1 + (Annual Interest Rate / Number of compounding periods per year))^(Number of compounding periods per year * Number of years) - Principal
Interest for the first 6 months = k4800 * (1 + (0.0885 / 12))^(12 * 0.5) - k4800
Interest for the first 6 months = k4800 * (1 + 0.0885/12)^6 - k4800
Interest for the first 6 months = k4800 * (1.007375)^6 - k4800
Interest for the first 6 months = k4800 * 1.0452 - k4800
Interest for the first 6 months ≈ k543.05
After 6 months, John will owe the interest of k543.05 on top of the principal amount.
Then, John is making a payment of k1000 every 6 months, so after making the first payment of k1000, the remaining balance would be:
Remaining balance = Initial principal + Interest accrued after 6 months - Payment
Remaining balance = k4800 + k543.05 - k1000
Remaining balance = k5337.05
Therefore, John will owe approximately k5337.05 after his first payment.