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 $670,000
Interest Rate 11.4%
Life 54 years
Date of Loan January 1, 2021
Use the installment method - not straight line
Do NOT round any interrmediate numbers.
Do NOT turn this into a monthly problem.
Do NOT put in minus signs, answer all positive numbers.
Required:
1. What is the annual payment (round to the nearest $)?
$ ____
2. What are the total interest payments (round to the nearest $)?
$ _____
3. After 34 payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)?
____ %
4. After 34 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 2%
(for a well designed spreadsheet this should take 30 seconds)
Required:
5. What is the annual payment (round to the nearest $)?
____$
6. What are the total interest payments (round to the nearest $)?
____$
7. After 34 payments have been made, what percentage of the total interest has been paid (round to the nearest percentage point)?
____ %
8. After 34 payments have been made, what percentage of the total principal has been paid (round to the nearest percentage point)?
____ %

Answer 1

Answer:

Loan = $670,000

Interest Rate = 11.4%

Years (Life) = 54 years

1. Loan = Annual installment * (1-(1+i)^-n)/i

$670,000 = Annual installment * (1-(1+11.4%)^-54)/11.4%

$670,000 = Annual installment * 8.74614912

Annual installment = $670,000 /8.74614912

Annual installment = 76605.14257

Annual installment = $76,605

2. Total interest payment = Total installments - Original loan

Total interest payment = $76605.14*54 - $670,000

Total interest payment = $4,136,677.56 - $670,000

Total interest payment = $3,466,677.699

Total interest payment = $3,466,678

3. Capital o/s after 34 payments = 76605.14257 × (1-(1+11.4%)^-20)/11.4%

= $594412.8888

Capital repaid = $670000 - $594412.8888 = $75587.11123

Total interest paid till 34 installments = $76605.14257*34 - $75587.11123 = $2528987.736

Percentage of interest = ($2528987.736/ ($76605.14257*54- $670000)) * 100

Percentage of interest = 0.7295133715

Percentage of interest = 72.95133715%

4. Percentage of principal = (75587.11123/670000)*100

Percentage of principal = 0.1128165839

Percentage of principal = 11.28165839%

Percentage of principal ≈ 11%