$12,000 due today is to be replaced by three equal payments in 30, 60 and 90 days from today. If interest is 8.4% annually, determine the value of the payments. Use a focal date of today.
A) $4,055.87
B) $4,165.26
C) $4,276.65
D) $4,387.42
E) $4,598.57

Question

Quizplus · Accepted Answer

To find the value of the payments, we use the present value formula for each payment and solve for the payment amount (PMT) that makes the sum of the present values equal to $12,000. The interest rate per day is $ \frac{8.4\%}{365} $. The present value (PV) formula is $ PV = \frac{PMT}{(1 + r)^n} $, where $ r $ is the daily interest rate and $ n $ is the number of days until the payment.1. For the payment in 30 days: $ PV_1 = \frac{PMT}{(1 + \frac{0.084}{365})^{30}} $2. For the payment in 60 days: $ PV_2 = \frac{PMT}{(1 + \frac{0.084}{365})^{60}} $3. For the payment in 90 days: $ PV_3 = \frac{PMT}{(1 + \frac{0.084}{365})^{90}} $The total present value is the sum of these, set equal to $12,000:$$ 12,000 = \frac{PMT}{(1 + \frac{0.084}{365})^{30}} + \frac{PMT}{(1 + \frac{0.084}{365})^{60}} + \frac{PMT}{(1 + \frac{0.084}{365})^{90}} $$Solving this equation for PMT gives the value of each payment. Using the given interest rate and the focal date of today, the calculation results in PMT = $4,055.87.

$12,000 Due Today Is to Be Replaced by Three Equal