Question

Carla earns $100,000 per year now and pays $20,000 per year on her fixed-rate mortgage. Her income is subject to a COLA clause. If the risk-free rate of interest is 3%, and the expected inflation rate is 2% per year, what is the spending power of her net income in 10 years, expressed in today's dollars? And how would you find the present value of 10 years of Carla's income without being given an inflation rate or interest rate? HINT: Use market data to determine your answer.

US market rate

Answer 1

Risk is the possibility that an actual outcomes may differ from the expected outcome therefore, a risk free rate is the certainity that an actual outcome will not differ from the expected outcome.

Nominal Rate(Risk free rate) = 3%

Inflation Rate = 2%

Real Rate = ?

Nominal Rate = Real Rate + Inflation Rate

3% = Real Rate + 2%

Real Rate = 3% - 2%

Real Rate = 1%

Carla earns = $100,000 per year

Fixed Mortage rate = 20000 per year

Remaining amount carla can spend = 80000 per year

Carla the spending power of her net income in 10 years, expressed in today's dollars real rate @ 1%

Remaining amount carla can spend = 80000 per year

Real rate = 1%

Period = 10 years

Spending power = 80000 * 9.471 = $ 757680

the present value of 10 years of Carla's income without being given an inflation rate or interest rate = 3%

Remaining amount carla can spend = 80000 per year

Nominal rate = 3%

Period = 10 years

Present value of carla's income = 80000 * 8.530 = $ 682400

Carla cost of inflation on purchasing power = 757680 - 682400 = 75280

Carla will be losing purchasing power due to inflation will be $ 75280 during the period of 10 years