A man's bank has offered him a loan of $20000 payable within the year at an annual interest rate of 24%. Calculate the monthly equal payment to defray both the principal and interest payment. Prepare a loan repayment schedule segregating interest from the principal.
20,000 x 24/100 = x (interest cost)
x/12=y (monthly cost of interest)
20,000/12=? (monthly cost of repaying principal)
Add y and ? to compute monthly repayment schedule.
To calculate the monthly equal payment to defray both the principal and interest payment, we can use the formula for Equal Monthly Installment (EMI):
EMI = (P * R * (1+R)^N) / ((1+R)^N - 1)
Where:
P = Principal amount (loan amount) = $20,000
R = Monthly interest rate = Annual interest rate / 12 / 100
N = Total number of payments = 12
Let's plug in the values to calculate the EMI:
R = 24% / 12 / 100 = 0.02
N = 12
EMI = (20,000 * 0.02 * (1+0.02)^12) / ((1+0.02)^12 - 1)
EMI = $1,934.60 (rounded to two decimal places)
Therefore, the monthly equal payment to defray both the principal and interest payment is approximately $1,934.60.
Now, let's prepare the loan repayment schedule segregating interest from the principal. Assuming we make the EMI payment for each month:
Month | Principal | Interest | Total Payment | Remaining Balance
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1 | $1,607.86 | $333.33 | $1,941.19 | $18,392.14
2 | $1,617.65 | $323.54 | $1,941.19 | $16,774.49
3 | $1,627.57 | $313.62 | $1,941.19 | $15,146.93
4 | $1,637.61 | $303.59 | $1,941.19 | $13,509.32
5 | $1,647.78 | $293.42 | $1,941.19 | $11,861.54
6 | $1,658.07 | $283.13 | $1,941.19 | $10,203.47
7 | $1,668.49 | $272.70 | $1,941.19 | $8,534.98
8 | $1,679.04 | $262.16 | $1,941.19 | $6,855.94
9 | $1,689.72 | $251.47 | $1,941.19 | $5,166.22
10 | $1,700.53 | $240.66 | $1,941.19 | $3,465.69
11 | $1,711.46 | $229.73 | $1,941.19 | $1,754.22
12 | $1,722.54 | $218.66 | $1,941.19 | $32.68
In the repayment schedule, you can see that each month the EMI payment remains constant and is used to cover both the principal and interest portions of the loan. As the principal decreases over time, the interest portion also decreases, and more of the EMI payment goes towards reducing the principal.
Note: The values in the table were rounded to two decimal places for simplicity.