Asked by Austin Guthrie on May 30, 2024
Verified
$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
Equal Payments
Regularly scheduled payments of the same amount over the term of a loan or mortgage.
Interest Annually
The amount of interest earned or paid over a one-year period, often expressed as a percentage of the principal.
- Investigate the benefits of multiple payment methods to make wise financial choices.
- Discriminate between present value and future value as applied in finance calculations.
Verified Answer
CD
Cindy DaisyJun 06, 2024
Final Answer :
A
Explanation :
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 8.4%365 \frac{8.4\%}{365} 3658.4% . The present value (PV) formula is PV=PMT(1+r)n PV = \frac{PMT}{(1 + r)^n} PV=(1+r)nPMT , where r r r is the daily interest rate and n n n is the number of days until the payment.1. For the payment in 30 days: PV1=PMT(1+0.084365)30 PV_1 = \frac{PMT}{(1 + \frac{0.084}{365})^{30}} PV1=(1+3650.084)30PMT 2. For the payment in 60 days: PV2=PMT(1+0.084365)60 PV_2 = \frac{PMT}{(1 + \frac{0.084}{365})^{60}} PV2=(1+3650.084)60PMT 3. For the payment in 90 days: PV3=PMT(1+0.084365)90 PV_3 = \frac{PMT}{(1 + \frac{0.084}{365})^{90}} PV3=(1+3650.084)90PMT The total present value is the sum of these, set equal to $12,000: 12,000=PMT(1+0.084365)30+PMT(1+0.084365)60+PMT(1+0.084365)90 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}} 12,000=(1+3650.084)30PMT+(1+3650.084)60PMT+(1+3650.084)90PMT 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.
Learning Objectives
- Investigate the benefits of multiple payment methods to make wise financial choices.
- Discriminate between present value and future value as applied in finance calculations.
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