Time Value of Money Practice Questions

Question 1

Carolyn is planning for her retirement. She is currently 37 years old and plans to retire at age 62 and hopes to live until age 97. She currently earns $100,000 per year and anticipates needing 80% of her income during retirement. She anticipates that Social Security will provide her with $15,000 per year starting at age 62, leaving her with required savings to provide $65,000 annually during retirement ($100,000 × 0.80 − $15,000). She believes she can earn 11% on her investments, and that inflation will be 2% per year. How much must Carolyn save at the end of each year if she wants to make her last savings payment at age 62 to meet her retirement goal, assuming she wants to maintain the original purchasing power of her capital balance?

Answer 1

$10,899

1. Determine funding need.
   - 100k * .8 = 80k - 15k = $65,000
2. Inflate income need to retirement age (set to END)
   - PV = $65,000
   - PMT = 0
   - N = 25 (67 retirement age - 37 current age)
   - I = 2 (not .02 or 2%)
   - Solve for FV = $106639.39
3. PV of retirement annuity (set to BEG)
   - PMT = 106,639.39
   - I = 1.11/ 1.02 = 1.088235 * 100 = 8.8235
   - FV = 0
   - N = 35
   - Solve for PV = $1,247,035.59
4. Annual funding amount
   - PDV = 1,247,035.59
   - N = 25
   - I = 11
   - PV = 0
   - Solve for PMT = 10,899.37

Question 2

Patricia hopes to save $75,000 for a down payment on a home. If she contributes $1,300 at the beginning of each month and earns a 5% annual return on her investment, compounded monthly, about how many months will it take her to reach her goal?

Answer 2

52 months

BEGIN Mode
P/YR = 12
N = ?
i = 5
PV = 0
PMT = <1,300>
FV = 75,000
51.6153

Question 3

Kyle borrows $75,000 from a friend to purchase a 25% ownership in a local brewery. If we assume the term of his loan is 10 years and he is required to make annual payments in the amount of $10,000, what is the implied interest rate on this loan?

Answer 3

5.6%

N: 10
PV: $75,000
PMT: ($10,000)
FV: $0
I: 5.60%

Question 4

Christian wants to retire in 15 years when he turns 65. Christian wants to have enough money to replace 75% of his current income less what he expects to receive from Social Security at the beginning of each year. He expects to receive $18,000 per year from Social Security in today’s dollars. Christian is aggressive and wants to assume an 8% annual investment rate of return and that inflation will be 3% per year. Based on his family history, Christian expects that he will reach the age of 95. If Christian currently earns $80,000 per year and he expects his raises to equal the inflation rate, how much does he need at retirement to fulfill his retirement goals?

Answer 4

$1,072,454

Step 1: Estimate the funding amount in today’s dollars
($80,000 x .75) = $60,000 - $18,000 = $42,000

Step 2: Inflate the need to the beginning of retirement.

PV: <42,000>
I/YR: 3
N: 15
PMT: 0
FV: 65,434.63

Step 3: Determine the funding need at retirement age.

BEGIN MODE
PMT: 65,434.63
I/YR: [(1.08/1.03) − 1] × 100 = 4.8544
N: 30
FV: 0
PV: <1,072,454.29>

Step 4: Determine the required annual savings amount.

END MODE
FV: 1,072,454.29
N: 15
I/YR: 8
PV: 0
PMT: <39,498>

Question 5

Contributing $1,500 to his retirement fund at the end of each year beginning at age 18 through age 50, with an average annual return of 12%, how much does Juan have in his retirement account at this time to use toward a possible early retirement?

Answer 5

$457,271.58

N=50 – 18 = 32
i=12
PV=0
Pmt=1,500
FV= <457,271.5789>