Final answer:
The equivalent value of a $124,000 payment due 14 months from today, if it is paid 5 months from today, is $135,452.87.
Step-by-step explanation:
To find the equivalent value of a $124,000 payment due 14 months from today if it is paid 5 months from today, we need to consider compound interest. The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the payment
- P is the present value of the payment (the initial amount)
- r is the annual interest rate (as a decimal)
- n is the number of compounding periods per year
- t is the number of years
In this case, the payment earns 10.5% interest compounded quarterly. So, r = 0.105, n = 4, and t = 14/12 = 1.1667 for the original payment date, and t = 5/12 = 0.4167 for the new payment date. Plugging these values into the formula, we get:
A = 124000(1 + 0.105/4)^(4 * 1.1667) = $137,356.06
A = 124000(1 + 0.105/4)^(4 * 0.4167) = $135,452.87
The equivalent value of the payment if it is paid 5 months from today instead is $135,452.87.