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

1. How much would she save? How much would she consume?
2. 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?
3. 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?
4. 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

Earning this year = $2,000

Earning next year = $1,500

Interest rate = 10%

a) Money saved in year 1 will save rate of interest for 1 year. Let say money saved in year 1 is X while money spent is 2,000 - X.

Spending in year 1 = 2,000 - X

Spending in year 2 = 1.1X + 1,500

2,000 - X = 1.1X + 1,500

X = 238.09

Money spent in year 1 = 1,761.9 while money saved is 238.09

b) Lottery won in year 1 raised income to $10,000

Let say money saved in X

Spending in year 1 = 10,000 - X

Spending in year 2 = 1.1X + 1,500

10,000 - X = 1.1X + 1,500

X = 4,047.61

Spending in year 1 = 10,000 - 4,047.61 = 5,952.38

Saving in year 1 = 4,047.61

c) If consumption in year 1 is twice that of year 2. Let say consumption in year 1 is 10,000 - X and saving is X. This X will earn rate of interest for one year.

Consumption in year 1 = 10,000 - X

Consumption in year 2 = 2 * (1.1X + 1,500) = 2.2X + 3,000

10,000 - X = 2.2X + 3,000

X = 2,187.5

Consumption in year 1 = 7,812.5

Saving in year 1 = 2,187.5

d) If she wants to save 5,000 in year 1 to buy car in year 2

Assume she consume equal quantity in both period. She save X out of 5,000 and consume 5,000 - X

5,000 - X = 1.1X + 1,500

X = 1,666.67

She save 1,666.67 out of 5,000 in year 1 and consume rest of the money.