ry pays 5000 at the end of every month to a bank as loan repayment the interest rate of 10% compounded monthly and t=4 months. Find the present value?
To find the present value, we need to calculate the total amount paid over the four months and then find the present value of that amount.
First, let's calculate the total amount paid over the four months, considering the interest rate and compounding:
1. Calculate the interest rate per period: 10% / 12 months = 0.10 / 12 = 0.00833
2. Calculate the total amount paid each month with interest: $5000 * (1 + 0.00833)^4 = $5000 * 1.03335 = $5166.77
3. Calculate the total amount paid over four months: $5166.77 * 4 = $20,667.08
Now, to find the present value, we need to discount this total amount back to the present. We'll assume the discount rate is the same as the interest rate, 10% compounded monthly.
1. Set up the present value formula: Present Value = Future Value / (1 + interest rate)^t
2. Calculate the present value: Present Value = $20,667.08 / (1 + 0.00833)^4
= $20,667.08 / (1.03335)^4
= $20,667.08 / 1.13471795214
= $18,199.71 (rounded to the nearest cent)
Therefore, the present value of the loan repayments is approximately $18,199.71.