Question

You borrow money on a self liquidating installment loan (equal payments at the end of each year, each payment is part principal part interest)
Loan amount: $776,000
Interest Rate: 11.6%
Life: 41 years
Date of Loan: January 1, 2021

Required:
1. What is the annual payment (round to the nearest $)?
2. What are the total interest payments (round to the nearest $)?
3. After 23 payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)?
4. After 23 payments have been made, what percentage of the total principal has been paid (round to the nearest percentage point)?

Redo the problem if the interest rate is 1%
Required:
5. What is the annual payment (round to the nearest $)?
6. What are the total interest payments (round to the nearest $)?
7. After 23 payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)?
8. After 23 payments have been made, what percentage of the total principal has been paid (round to the nearest percentage point)?

Answer 1

The annual payment on the loan is $108943.

How to calculate the loan?

Principal = $776000

Rate = 11.6%

Time = 41 years

The total interest will be:

= PRT/100

= (776000 × 11.6 × 41)/100

= $3690656

The total amount to be paid will be:

= $776000 + $3690656

= $4466656

The annual payment will be:

= Total amount / Number of years

= $4466656 / 41

= $108943

After 23 years, the interest will be:

= 776000 × 11.6 × 23)/100

= $2070368

The percentage of the total interest will be:

= $2070368/$3690656

= 56.1%

When 23 payments have been made, the percentage of the total amount will be:

= (776000 + 2070368) / 4466656

= 2846368/4466656

= 63.72%

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