Question

3. Suppose Reuben earned a salary of $50,000 in 2015 and $55,000 in 2016.

a) The consumer price index was 120 in 2015 and 132 in 2016. What has happened to Reuben’s nominal and real income from 2015 to 2016? Show your work. –

b) Suppose Reuben owed student loans that had an interest rate of 3 percent. What was the real interest rate on Reuben’s student loans for 2015-2016. Show your work.

Answer 1

(A)The information given in the question relating to salary of Ruben can be classified in the below table

Year	Ruben’s salary (Nominal income)	Consumer price index (CPI)	Ruben’s real income = (Nominal Income/CPI)x100
2015	$50,000	120	$41,666.67
2016	$55,000	132	$41,666.67

1. It is clearly evident that Ruben’s Nominal income or the income without inflation adjusted increase from year 2015 to 2016.

2. It is clearly evident that Ruben’s Real income or the income adjusted for inflation remains same or unchanged from year 2015 to 2016.

(B) As per the question Ruben owned a loan with an interest rate (Nominal Interest) =3% = 0.03

Inflation rate between period 2015 to 2016 = {(CPI of 2016-CPI of 2015)/CPI of 2015)x100

Inflation rate between period 2015 to 2016 = {(132-120)/120)x100= 10% = 0.10

Rea interest can be calculated in two methods

The basic formula for calculating real interest is = Nominal rate- inflation rate = 3%-10%=-7%

But the more precise formula for calculating real interest is

Real interest rate = {(1+Nominal interest rate)/(1+ inflation rate)}-1 =(1+0.03/1+ 0.10)-1

Real interest rate = (1.03/1.1)-1= 0.9364-1=-0.0636= -6.36%

The real interest rate of Ruben’s student loan for year 2015 to 2016 is -6.36%