Question
Joe applied a loan amount of K2500 with bsp at the rate of10%p.a and regular payment of K850 at the end of every year after the interest is credited. What is the total interest paid within the loan period? Show your working out not step by step
Answers
GPT-4o mini
To calculate the total interest paid by Joe on his loan amount of K2500 with a 10% annual interest rate and regular payments of K850 at the end of each year, we can utilize the amortization formula for loans.
First, we need to calculate the interest accrued each year on the outstanding balance of the loan.
1. **Initial Loan Amount**: K2500
2. **Interest Rate**: 10% per annum
3. **Annual Payment**: K850
Each year, interest is charged on the remaining balance of the loan. The interest for the first year would be:
Interest for Year 1 = Loan Amount × Interest Rate
= K2500 × 10% = K250.
The remaining balance after the first payment would be:
New Balance = Previous Balance + Interest - Payment
= K2500 + K250 - K850 = K1900.
For the second year, the interest is calculated on the new balance:
Interest for Year 2 = K1900 × 10% = K190.
New Balance after Year 2 payment:
= K1900 + K190 - K850 = K1240.
For the third year:
Interest for Year 3 = K1240 × 10% = K124.
New Balance after Year 3 payment:
= K1240 + K124 - K850 = K514.
For the fourth year:
Interest for Year 4 = K514 × 10% = K51.4.
New Balance after Year 4 payment:
= K514 + K51.4 - K850 = -K284.6 (this means the loan is paid off before the fourth payment).
To summarize the interest paid over the years:
- Year 1 Interest = K250
- Year 2 Interest = K190
- Year 3 Interest = K124
- Year 4 Interest = K51.4
- Total Interest Paid = K250 + K190 + K124 + K51.4 = K615.4.
Thus, the total interest paid by Joe over the life of the loan is **K615.4**.
First, we need to calculate the interest accrued each year on the outstanding balance of the loan.
1. **Initial Loan Amount**: K2500
2. **Interest Rate**: 10% per annum
3. **Annual Payment**: K850
Each year, interest is charged on the remaining balance of the loan. The interest for the first year would be:
Interest for Year 1 = Loan Amount × Interest Rate
= K2500 × 10% = K250.
The remaining balance after the first payment would be:
New Balance = Previous Balance + Interest - Payment
= K2500 + K250 - K850 = K1900.
For the second year, the interest is calculated on the new balance:
Interest for Year 2 = K1900 × 10% = K190.
New Balance after Year 2 payment:
= K1900 + K190 - K850 = K1240.
For the third year:
Interest for Year 3 = K1240 × 10% = K124.
New Balance after Year 3 payment:
= K1240 + K124 - K850 = K514.
For the fourth year:
Interest for Year 4 = K514 × 10% = K51.4.
New Balance after Year 4 payment:
= K514 + K51.4 - K850 = -K284.6 (this means the loan is paid off before the fourth payment).
To summarize the interest paid over the years:
- Year 1 Interest = K250
- Year 2 Interest = K190
- Year 3 Interest = K124
- Year 4 Interest = K51.4
- Total Interest Paid = K250 + K190 + K124 + K51.4 = K615.4.
Thus, the total interest paid by Joe over the life of the loan is **K615.4**.