Time Value of Money Questions Flashcards
Bob is a fisherman with the local fish market. He and his wife Mary want to retire in 20 years. They expect to live approximately 25 years after retirement and need $40,000 (in today's dollars) annually during retirement. Unfortunately, they have just spent their savings on refurbishing their boathouse and have only $12,000 in retirement savings. Inflation is currently 2% and is expected to continue indefinitely. Bob believes he can earn an 8% rate of return before retirement but expects to earn only 6% during retirement because of the change in his portfolio's asset allocation at retirement. How much does Bob need to save at the end of each year to meet his retirement needs? A) $20,374. B) $20,040. C) $44,147. D) $29,763.
B
Using the three-step method to solve.
Step 1: Inflate needs until retirment:
PV = −40,000 n = 20 i = 2 FV = 59,437.90 Step 2: Discount annual needs to beginning of retirement:
BEG mode
PMT = 59,437.90
n = 25
i =[(1.06 ÷ 1.02) − 1} × 100 (inflation-adjusted discount rate)
PVAD = 973,006.62
Step 3: Determine the annual funding requirement:
FV = $973,006.62 PV = −12,000 n = 20 i = 8 PMT = 20,040.11, or $20,040.11
A couple wants to accumulate a retirement fund of $300,000 in today’s dollars in 18 years. They expect inflation to be 4% per year during that period. If they set aside $20,000 at the end of each year and earn a 6% after-tax rate of return on their investment, will they reach their goal?
A)
No, they will accumulate $10,368 less than needed.
B)
Yes, they will accumulate $10,368 more than needed.
C)
Yes, they will accumulate $47,454 more than needed.
D)
No, they will accumulate $47,454 less than needed.
B
At 10% interest with annual compounding, approximately how long will it take for $1 to grow to $100 (round to the nearest year)? A) 48 years. B) 57 years. C) 38 years. D) 53 years.
A
Tom and Mary Jane want to purchase a beach house in 5 years. They know they will have to accumulate at least $150,000 in today's dollars. They expect to earn a 10% after-tax rate of return (compounded annually) and anticipate an average annual inflation rate of 4%. They want to make substantially equal payments, adjusted for inflation, at the end of each year. What serial payments will they have to make at the end of years 2 and 5, respectively? (Round to the nearest dollar) A) $30,070 and $31,273. B) $28,914 and $32,524. C) $26,732 and $27,801. D) $27,801 and $28,913.
B
END mode FV = 150,000 PV = 0 i = 5.7692 [(1.10 ÷ 1.04) - 1] × 100 n = 5 PMT = (26,732.35) $26,732.35 × 1.04 = $27,801.64 = Payment at end of year 1
Payment at end of year 2 = $27,801.64 × 1.04 = $28,913.71
Payment at end of year 3 = $28,913.71 × 1.04 = $30,070.26
Payment at end of year 4 = $30,070.26 × 1.04 = $31,273.07
Payment at end of year 5 = $31,273.07 × 1.04 = $32,523.99
A client is to receive $650 per month for five years at the beginning of each month beginning one year from today. What is the present value of all payments (rounded to the nearest dollar), assuming an annual discount rate of 9%? A) $34,387. B) $30,339. C) $31,548. D) $28,943.
D
Step 1: Calculate the present value of an annuity of $650 per month for 60 months at a discount rate of 9%.
BEG mode PMT = 650 i = 0.75 (9 ÷ 12) n = 60 (5 × 12) Solve for PVAD = 31,548 This provides the present value of an annuity one year from now.
Step 2: This amount is further discounted to the present, one year.
FV = 31,548 PMT = 0 i = 9 n = 1 Solve for PV = 28,943, or $28,943
