Joe 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 after straight after his:
First payment?
Second payment?
Third payment?
To calculate the amount Joe owes after each payment, we will need to calculate the new balance after each payment is made.
Initially, Joe owes k4800. The interest is compounded monthly, so the monthly interest rate is 8.85%/12 = 0.7375%.
First Payment:
After the first 6 months, Joe will have made a k1000 payment. The interest for the first 6 months will accumulate on the remaining balance of k4800 - k1000 = k3800.
The interest for the first month = 0.007375 * 3800 = k28.03
The total amount Joe owes after the first payment = k3800 + k28.03 + k1000 = k4828.03
Second Payment:
After the second 6 months, Joe will make another k1000 payment. The interest for the second 6 months will accumulate on the remaining balance of k4828.03 - k1000 = k3828.03.
The interest for the second month = 0.007375 * 3828.03 = k28.25
The total amount Joe owes after the second payment = k3828.03 + k28.25 + k1000 = k4856.28
Third Payment:
After the third 6 months, Joe will make another k1000 payment. The interest for the third 6 months will accumulate on the remaining balance of k4856.28 - k1000 = k3856.28.
The interest for the third month = 0.007375 * 3856.28 = k28.45
The total amount Joe owes after the third payment = k3856.28 + k28.45 + k1000 = k4884.73
Therefore, Joe will owe:
- k4828.03 after the first payment
- 4856.28 after the second payment
- 4884.73 after the third payment