Asked by Cassandra Ramirez on Apr 28, 2024
Verified
Your uncle left you an inheritance in the form of a trust. The trust agreement states that you are to receive $750 each year, starting today and continuing for 25 years. What is the value of this inheritance today if the applicable discount rate is 5.8%?
A) $9,772.46
B) $9,989.82
C) $10,339.26
D) $10,623.33
E) $11,004.28
Discount Rate
A rate used to determine the present value of future cash flows; in monetary policy, it refers to the interest rate charged to commercial banks for loans from a central bank.
Trust Agreement
A legal document establishing a trust and outlining the rules and guidelines that the trustees must follow in managing the trust assets for the benefit of the beneficiaries.
- Evaluate the immediate and prospective economic values of lump sums, recurring payments, and perpetual financial streams.
- Assess the valuation of scholarships, trusts, and retirement accounts given diverse financial circumstances.
Verified Answer
RM
Raquel MartinezApr 30, 2024
Final Answer :
C
Explanation :
This is an annuity due problem since the payments start today. The present value of an annuity due can be calculated using the formula: PV=P×(1−(1+r)−nr)×(1+r)PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)PV=P×(r1−(1+r)−n)×(1+r) , where PPP is the payment amount, rrr is the discount rate per period, and nnn is the number of periods. Plugging in the values: PV=750×(1−(1+0.058)−250.058)×(1+0.058)PV = 750 \times \left(\frac{1 - (1 + 0.058)^{-25}}{0.058}\right) \times (1 + 0.058)PV=750×(0.0581−(1+0.058)−25)×(1+0.058) , we get a present value of approximately $10,339.26, which matches option C.
Learning Objectives
- Evaluate the immediate and prospective economic values of lump sums, recurring payments, and perpetual financial streams.
- Assess the valuation of scholarships, trusts, and retirement accounts given diverse financial circumstances.