Not sure how to solve:
Two Questions:
(1)Cindy has income of $12000 in year 0.
Calculate her income in year 1 if she wants to consume $26,000 in year 0 and $14,000 in year 1. Assume the interest rate is 4% per year.
(2)Jonathan has income of $45000 in period 0 and $65000 in period 1. An investment opportunity that costs $30000 in period 0 is worth $32000 in period 1. What is the maximum possible consumption in period 0 if Jonathan consumes $70000 in period 1 when the market rate of interest in 4%?
Are you sure you've copied these questions correctly?
Consume means to use up. How can she "consume" over twice her income in year 0?
Is she earning or paying 4% interest?
The second question is just as confusing.
Where are you getting these questions?
This is how I interpret your question #1.
(1) Cindy starts year 1 with a debt of $26,000-12,000 = $14,000 from year 0, or a bit less if she has been making minimum payments on the loan or credit card that she uses to pay the bills. If she is lucky enough to get 4% financing (which is unlikely, judging by her spending habits), and she wants to pay her debt off by the end of year 1, then she will have to pay off about 14,280 during year 2. That is 14,000 + (average yr. 0 balance x 4%). She also needs 14,000 for consumption in year 1, so she will need to earn $8,280. She'd better start looking for a higher paying job.
This reads like a student loan type of situation, in which case there is no requirement to pay off the loan at the end of year 1. Cindy might choose to pay interest only on the loan during year 1 without increasing the loan balance, or to go further in debt, if allowed to do so. This question requires a lot more information to answer accurately.
typo: $8280 should be $28,280 in the first paragraph. My computer erased the 2 when I inserted the $
Thanks for the responses. This (Finance) professor is notorious for using ambiguous problems.
(2) The 6.7% capital gain on the investment barely covers the 4% interest rate loan that made the investment possible, so let's just ignore it. The profit is less tan $1000.
ASSUMING that Jonathan wants to end year 1 without debt, then his two-year income of 110,000 should match or exceed his two-year consumption of 70,000 + X. X, the first-year consumption, should not exceed $40,000.
The answer you get depends upon assumptions that have to be made, because the "ground rules" of the problem are not clearly stated.
Will if your in shiller's class at UNB than ignore these answers they are all wrong
To solve these questions, we can use the concept of present value and future value. The present value is the current value of an amount of money, and the future value is the value of that money at a later date, after accounting for interest.
Question 1:
To calculate Cindy's income in year 1, we need to find the amount of money she needs to save and invest today, so it can grow to cover her consumption in year 1. We'll use the present value formula for this calculation.
Given:
Income in year 0 (Cindy's current income): $12,000
Consumption in year 0 (current year): $26,000
Consumption in year 1 (future year): $14,000
Interest rate: 4% per year
Step 1: Calculate the present value of Cindy's consumption in year 0.
PV = FV / (1 + r)^n
PV = $26,000 / (1 + 0.04)^0
PV = $26,000 / 1
PV = $26,000
Step 2: Calculate the present value of Cindy's consumption in year 1.
PV = FV / (1 + r)^n
PV = $14,000 / (1 + 0.04)^1
PV = $14,000 / 1.04
PV = $13,461.54 (rounded to the nearest cent)
Step 3: Calculate Cindy's total income in year 1.
Total Income = Current Income + Present Value of Future Consumption
Total Income = $12,000 + $13,461.54
Total Income = $25,461.54
Therefore, Cindy's income in year 1 will be approximately $25,461.54.
Question 2:
To calculate the maximum possible consumption in period 0, we need to find the present value of Jonathan's future consumption in period 1 and subtract it from his period 0 income. We'll use the present value formula again.
Given:
Income in period 0: $45,000
Income in period 1: $65,000
Consumption in period 1: $70,000
Investment cost in period 0: $30,000
Investment value in period 1: $32,000
Interest rate: 4% per year
Step 1: Calculate the present value of Jonathan's consumption in period 1.
PV = FV / (1 + r)^n
PV = $70,000 / (1 + 0.04)^1
PV = $70,000 / 1.04
PV = $67,307.69 (rounded to the nearest cent)
Step 2: Calculate Jonathan's maximum possible consumption in period 0.
Maximum Consumption in period 0 = Income in period 0 - Present Value of Future Consumption
Maximum Consumption = $45,000 - $67,307.69
Maximum Consumption = -$22,307.69
Note: The negative value indicates that Jonathan's income in period 0 is not enough to cover his consumption in period 1.
Therefore, Jonathan cannot afford to consume $70,000 in period 1 if his income in period 0 is $45,000 and the market interest rate is 4%.