Question

On January 1, 2017 Diana invested $1,000 at 6% interest per year for three years.

The CPI on January 1, 2017 was 100. On January 1, 2018 the CPI was 104; on January 1, 2019 it was 109; and on January 1, 2020, the day Diana’s investment matured, the CPI was 115.

Find the real rate of interest earned by Diana in each of the 3 years and her total real return over the three-year period. Assume that interest earnings are reinvested each year and that they themselves earn interest. Express your answers in tenths of one percent, e.g. 1.1 %

Hint: create a table with one column inflation and the next the real return and a third column 1 + real return) for each of the three years in the problem.

Answer 1

Amount invested on 1 Jan 2017 = $1000
Intrest = 6%
time = 3 years
Before making a table, firstly focus on a line that is given in the above question that is interest earnings are reinvested each year and Diana earn interest. It means that each year interest will be different.
Now,
We know that
Rate of Inflation = (CPI_x+1 - CPI_x ) / CPI_x
Real return (interest) rate = {(1+ Nominal Rate) / (1+ Inflation Rate)} - 1
So, using these formulas, the below table is created.

Year	Amount	CPI	Inflation (CPIx+1 - CPIx ) / CPIx	Real Return {(1+ Nominal Rate) / (1+ Inflation Rate)} - 1	1+ real return
1 Jan 2017	$1000	100	---	---	---
1 Jan 2018	$1060	104	4%	1%	5%
1 Jan 2019	$1123.6	109	4.8%	1.1%	5.9%
1 Jan 2020	$1191.01	115	5.5%	0.4%	5.9%