A business invests $8,000 into an account that has 5% interest per-year. Annual inflation is 3.5 % over the next 5 years. Determine the inflation rate per half year?
I tried doing this:
MARR_R = (1+MARR_C)/(1+f) - 1
--> 6% = (1+MARR_C)/(1+3.5%) - 1
--> MARR_C = 9.71 %/yr = 9.71/2 %/6month = 4.86 %/6month.
But I got the answer wrong since none of the multiple choice answers were that value.
The question was multiple choice, and here were the answers:
(a) 9.71 %
(b) 5.67 %
(c) 8.26 %
(d) 4.74 %
Could somebody clarify how to do this properly? Thanks.
***Correction for the "Determine the inflation rate per half year":
The question asked for the actual/current MARR per half-year, not the inflation rate.
Sorry, another part I forgot to write (mixed it up with a similar question right by this question):
The real MARR (MARR_R) is given to be 6%.
What I wrote for the answer choices and my attempt at a solution still apply though.
To determine the inflation rate per half-year, we need to adjust the annual inflation rate to a semi-annual rate.
Let's break it down step by step:
Step 1: Convert the annual inflation rate to a half-year rate
To convert the annual inflation rate to a semi-annual rate, we need to divide it by the number of compounding periods in a year. In this case, we have two compounding periods (half-yearly).
Annual Inflation Rate = 3.5%
Semi-Annual Inflation Rate = Annual Inflation Rate / 2 = 3.5% / 2 = 1.75%
Step 2: Determine the nominal interest rate per half-year
The nominal interest rate is the sum of the inflation rate and the real interest rate. In this case, the real interest rate is the annual interest rate minus the annual inflation rate.
Annual Interest Rate = 5%
Real Interest Rate = Annual Interest Rate - Annual Inflation Rate = 5% - 3.5% = 1.5%
Now, let's determine the nominal interest rate per half-year:
Nominal Interest Rate = Real Interest Rate + Semi-Annual Inflation Rate
Nominal Interest Rate = 1.5% + 1.75% = 3.25%
So, the nominal interest rate per half-year is 3.25%.
Step 3: Check the answer options
Now let's compare the calculated value with the answer options given:
(a) 9.71% - This option is incorrect.
(b) 5.67% - This option is incorrect.
(c) 8.26% - This option is incorrect.
(d) 4.74% - This is the closest option, but it doesn't match our calculated value of 3.25%.
It seems that none of the provided answer options are correct based on our calculations. It's possible that there might be an error in the given answer choices, or there might be a mistake in the question itself.
In summary, the inflation rate per half-year should be 3.25% based on the provided information, but none of the given answer choices match this value.