Asked by Orion Lavigne on May 01, 2024
Verified
If money is worth 14 %, what payment on August 29 would be equal in value to a payment of $86,900 due on January 31 of the following year?
A) $74,734
B) $92,066
C) $81,734
D) $76,519
E) $82,024
Equal Value
A condition or state where two or more items, services, or amounts have the same worth or significance.
Due Payment
The amount of money that is scheduled to be paid at a certain date as part of a financial obligation.
- Comprehend the principle of equivalent value across various time intervals when factoring in the interest rate.
Verified Answer
UC
Ushmita ChettriMay 01, 2024
Final Answer :
E
Explanation :
To find the equivalent value of a future payment today, we need to discount the future payment by the interest rate over the period it is due. The period from August 29 to January 31 of the following year is approximately 5 months. Using the formula for discounting: Present Value = Future Value / (1 + r)^n, where r is the monthly interest rate and n is the number of months. Assuming the interest rate is annual, we convert it to a monthly rate by dividing by 12. Thus, r = 14% / 12 = 1.1667% per month. n = 5 months. Plugging in the values: Present Value = $86,900 / (1 + 0.14/12)^5. Solving this gives us approximately $82,024, making option E the correct choice.
Learning Objectives
- Comprehend the principle of equivalent value across various time intervals when factoring in the interest rate.