Tom bought a car wash in is 800,000 using a loan from credit corporation he was to pay back using four equal yearly installment of shillings 200,000 the render charged compound interest at a rate of 16% and a ledger fee at 15% per annum on the any outstanding balance at the time when each installment is paid what is the total amount of money paid at Tom to clear the loan
The total loan amount is 800,000 shillings. Since there are four equal yearly installments of 200,000 shillings, Tom will pay back 200,000 shillings per year.
Now, let's calculate the compound interest and ledger fees for each installment:
- For the first installment, Tom will owe 800,000 shillings (loan amount) + 800,000 shillings * 16% (compound interest) + 800,000 shillings * 15% (ledger fee) = 800,000 + 128,000 + 120,000 = 1,048,000 shillings.
- For the second installment, Tom will owe the previous balance of 1,048,000 shillings + 1,048,000 shillings * 16% (compound interest) + 1,048,000 shillings * 15% (ledger fee) = 1,048,000 + 167,680 + 157,200 = 1,372,880 shillings.
- For the third installment, Tom will owe the previous balance of 1,372,880 shillings + 1,372,880 shillings * 16% (compound interest) + 1,372,880 shillings * 15% (ledger fee) = 1,372,880 + 219,660.8 + 205,932 = 1,798,472.8 shillings.
- For the fourth and final installment, Tom will owe the previous balance of 1,798,472.8 shillings + 1,798,472.8 shillings * 16% (compound interest) + 1,798,472.8 shillings * 15% (ledger fee) = 1,798,472.8 + 287,755.65 + 269,770.92 = 2,356,999.37 shillings.
Therefore, the total amount of money paid by Tom to clear the loan is 200,000 shillings (first installment) + 1,048,000 shillings + 1,372,880 shillings + 1,798,472.8 shillings + 2,356,999.37 shillings = 6,575,352.17 shillings.
To calculate the total amount of money Tom paid to clear the loan, we need to consider the compound interest and the ledger fee.
Let's break down the calculations step-by-step:
1. Loan Amount: Tom bought the car wash for 800,000 shillings.
2. Installments: He needs to pay back the loan in four equal yearly installments of 200,000 shillings each.
Now let's calculate the interest and ledger fee for each installment:
3. First Installment: Tom will pay 200,000 shillings in the first year.
- Interest: The compound interest charged by the credit corporation is 16% per annum. Therefore, the interest for the first year would be (16/100) * 800,000 = 128,000 shillings.
- Ledger Fee: The ledger fee charged by the credit corporation is 15% per annum. Therefore, the ledger fee for the first year would be (15/100) * (800,000 - 200,000) = 90,000 shillings. (Here, we deduct the installment amount already paid from the outstanding balance before calculating the ledger fee.)
4. Second Installment: Tom will pay 200,000 shillings in the second year.
- Interest: The interest for the second year would be (16/100) * (800,000 - 200,000) = 96,000 shillings.
- Ledger Fee: The ledger fee for the second year would be (15/100) * (800,000 - 400,000) = 60,000 shillings.
5. Third Installment: Tom will pay 200,000 shillings in the third year.
- Interest: The interest for the third year would be (16/100) * (800,000 - 400,000) = 64,000 shillings.
- Ledger Fee: The ledger fee for the third year would be (15/100) * (800,000 - 600,000) = 30,000 shillings.
6. Fourth Installment: Tom will pay 200,000 shillings in the fourth year.
- Interest: The interest for the fourth year would be (16/100) * (800,000 - 600,000) = 32,000 shillings.
- Ledger Fee: The ledger fee for the fourth year would be (15/100) * (800,000 - 800,000) = 0 shillings.
Finally, let's calculate the total amount Tom paid to clear the loan by adding up the installments, interest, and ledger fees:
Total Amount = Installments + Interest + Ledger Fees
= (200,000 * 4) + (128,000 + 96,000 + 64,000 + 32,000) + (90,000 + 60,000 + 30,000 + 0)
= 800,000 + 320,000 + 180,000
= 1,300,000 shillings
Therefore, the total amount of money Tom paid to clear the loan is 1,300,000 shillings.