Question

1) Helena earns $2000 this year and will earn $1500 the next year. The interest rate between each year is 10%. She wants to consume the same quantity each year. She wants to have spent all her money by the end of year 2. Warning: each question does build on each other a) How much would she save? How much would she consume? b) If she wins the lottery during the first year, raising her earnings to $10000 this year, how much would she save, how much would she consume? c) If she now wants to consume twice as much in year 1 as she does in year 2, how much would she save, how much would she consume? d) If she now has no preferences about her consumption, but she wants to save $5000 in year 1 (to buy a new car in year 2), how much would she consume in year 1 and year2?

Answer 1

A] Income of current year = 2000

Let the amount used for consumption (in current year) be = x

So, the amount saved (in current year) = 2000 - x {Used next year}

Interest on current year savings = 10% (2000 - x) {Used next year}

As given, saving is done, as such consumption for both the years are equal :

Current year consumption = Next year consumption + current year savings + interest on current savings

x = 1500 + (2000 - x) + 10% (2000 - x)

x = 1500 + 2000 - x + 200 - 0.1x

x + 1.1x = 3700

2.1x = 3700

x = 1762 [Current year consumption] ; Current year saving = 2000 - x 2000 - 1762 = 238

Next year consumption = 1500 + saving + interest = 1500 + 238 + 24 = 1762. [Hence, Solved, Proved]

B] Similarly, for current year income = 10000 :

x = 1500 + (10000 - x) + 10% (10000 - x)

x = 1500 + 1.1 (10000 - x)

2.1x = 12500

x = 5952 [Current year consumption] ; Current year saving = 4048

Next year consumption = 1500 + 4048 + 404 = 5953 [Hence, Solved, Proved]