Mr. A has taken a car on lease. The down payment is80% of Total amount which is 200000rs. it is mutually agreed that 24equal payments would be made for the remaining amount by paying first installment todcay. which would be in addition to the down payment. the duration of the down payment be every quarter and interest rate is 19% compounded monthly. calculate inatallmants and construct amortization schedule.
To calculate the installments and construct an amortization schedule, we need to make a few calculations and assumptions. Here's how you can do it step by step:
1. Calculate the total lease amount:
The down payment is 80% of the total amount, which is given as 200,000 rs. So, we can calculate the total amount using the formula:
Total Amount = Down Payment / (1 - Down Payment Percentage)
Total Amount = 200,000 / (1 - 0.80)
Total Amount = 200,000 / 0.20
Total Amount = 1,000,000 rs.
2. Calculate the interest for each quarter:
The interest rate is 19% compounded monthly, so we need to use the compound interest formula:
Quarterly Interest Rate = (1 + Monthly Rate)^3 - 1
Monthly Rate = Annual Rate / 12
Monthly Rate = 19% / 12 = 0.019/12 = 0.001583
Quarterly Interest Rate = (1 + 0.001583)^3 - 1
Quarterly Interest Rate = 0.004749
3. Calculate the quarterly installments:
Since there are 24 equal payments over the lease period, we can divide the remaining amount (Total Amount - Down Payment) by 24 to get the quarterly installment:
Remaining Amount = Total Amount - Down Payment
Remaining Amount = 1,000,000 - 200,000 = 800,000 rs.
Quarterly Installment = Remaining Amount / Number of Payments
Quarterly Installment = 800,000 / 24 = 33,333.33 rs.
4. Construct the amortization schedule:
To construct the amortization schedule, we need to calculate the interest and principal amount for each payment.
a. First, calculate the interest for the first payment:
Interest Payment = Remaining Amount * Quarterly Interest Rate
Interest Payment = 800,000 * 0.004749 = 3,799.20 rs.
b. Next, calculate the principal amount for the first payment:
Principal Payment = Quarterly Installment - Interest Payment
Principal Payment = 33,333.33 - 3,799.20 = 29,534.13 rs.
c. Now, calculate the remaining balance after the first payment:
Remaining Balance = Remaining Amount - Principal Payment
Remaining Balance = 800,000 - 29,534.13 = 770,465.87 rs.
d. Repeat steps a, b, and c for the remaining payments, adjusting the Remaining Amount and Remaining Balance accordingly.
Here's an example of the amortization schedule for the first three payments:
| Payment No. | Installment | Principal Payment | Interest Payment | Remaining Balance |
|-------------|-------------|------------------|------------------|------------------|
| 1 | 33,333.33 | 29,534.13 | 3,799.20 | 770,465.87 |
| 2 | 33,333.33 | ... | ... | ... |
| 3 | 33,333.33 | ... | ... | ... |
| ... | ... | ... | ... | ... |
| 24 | 33,333.33 | ... | ... | ... |
Please note that the amortization schedule provided above is incomplete as it requires further calculations and details for each payment.