You borrow $2,500. you are to pay back the loan in 36 monthly payments of $79.50. what true annual interest are you paying to th
2 answers:
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Answer:
a. 23%.
b. Frank should charge Sarah 2% more than the inflation rate.
Explanation:
a. Find the nominal rate of interest.
To find this value we must follow this equation:
Where NI = Nominal Interest, RI= Real Interest, and IR= Inflation Rate.
a.1. Find the real interest rate.
The problem statement gives us this value: 2% real return per year, as agreed by Sarah and Frank.
a.2. Find the inflation rate.
Here we follow this equation:
Where:
CPI(F) is the CPI of the final year, in this case, it would be 121 (the expected CPI for two years, which is the established loan time).
CPI (B) is the CPI of the base year, that is, the CPI in force at the time that Frank makes the loan, 100 in this case.
We replace these values:
The inflation rate equals 21%.
a.3. Replace in the equation of the nominal rate of interest.
So, the nominal rate of interest Frank should charge Sarah equals 23%.
b. Find out how much Frank should charge Sarah (regarding inflation and considering that it is unknown).
The inflation rate reduces the return expected by Frank. Therefore, the nominal interest rate charged must be higher than the inflation rate, in order to ensure a positive real returns. In this case, since it is not known exactly what that inflation rate is, Frank must charge 2% (expected return) above what the inflation rate can record.
Hence, the short answer is: Frank should charge Sarah 2% more than the inflation rate.