You have two options available in repaying a loan.You can pay $2000 at the end of 5-months and $3000 at the end of 10-months OR you can pay $X at the end of 2-months and $3X at the end of 9-months.If the simple interest rate is r = 4% and the focal date is at the end of 5-months,what is X?
A)$1246.89
B)$2479.32
C)$2685.41
D)$2727.19

Question

Quizplus · Accepted Answer

To find the value of X, we need to equate the present value of both payment options using the given interest rate and focal date. The formula for the present value (PV) of a future payment is PV = FV / (1 + r)^t, where FV is the future value, r is the interest rate per period, and t is the time in periods until the payment.For the first option, the payments are $2000 at the end of 5 months (which is the focal date, so its present value is simply $2000) and $3000 at the end of 10 months. To find the present value of the $3000 payment, we adjust the interest rate to a monthly rate (since 4% is an annual rate) which is 4%/12 = 0.33% per month, and then calculate its present value 5 months before the focal date (since the focal date is at the end of 5 months and the payment is at the end of 10 months):PV = $3000 / (1 + 0.0033)^5 ≈ $2923.11So, the total present value of the first option is $2000 + $2923.11 = $4923.11.For the second option, we need to find the present value of $X at the end of 2 months and $3X at the end of 9 months, both relative to the focal date at the end of 5 months. For $X at the end of 2 months, this is 3 months before the focal date:PV of $X = X / (1 + 0.0033)^3For $3X at the end of 9 months, this is 4 months after the focal date, so we find its present value 4 months before the focal date:PV of $3X = $3X / (1 + 0.0033)^4The total present value of the second option is the sum of these, which we set equal to the total present value of the first option ($4923.11):X / (1 + 0.0033)^3 + $3X / (1 + 0.0033)^4 = $4923.11Solving this equation for X gives us the value of X. The correct calculation involves solving for X in the context of the given interest rates and time periods, which results in X being approximately $1246.89.

You Have Two Options Available in Repaying a Loan