Suppose you borrow $900 of principal that must be repaid at the end of two years, along with interest of 5 percent a year. If the annual inflation rate turns out to be 10 percent,
(a) What is the real rate of interest on the loan?
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To determine the real rate of interest on the loan, we need to account for the effect of inflation. The real rate of interest is the nominal interest rate (5 percent) adjusted for the inflation rate (10 percent).
Step 1: Calculate the nominal interest amount.
The nominal interest is calculated by multiplying the principal amount ($900) by the nominal interest rate (5 percent) and the duration of the loan (2 years).
Nominal interest = Principal × Nominal interest rate × Time
Nominal interest = $900 × 0.05 × 2 = $90
Step 2: Calculate the inflation-adjusted principal.
To account for inflation, we need to adjust the principal amount based on the inflation rate. The inflation-adjusted principal can be calculated using the following formula:
Adjusted principal = Principal / (1 + Inflation rate)
Adjusted principal = $900 / (1 + 0.10) = $900 / 1.10 = $818.18 (rounded to the nearest cent)
Step 3: Calculate the real rate of interest.
The real rate of interest can be found by dividing the nominal interest by the inflation-adjusted principal, and then multiplying by 100 to express it as a percentage.
Real rate of interest = (Nominal interest / Adjusted principal) × 100
Real rate of interest = ($90 / $818.18) × 100 ≈ 10.98%
Therefore, the real rate of interest on the loan, considering the 5 percent nominal interest rate and 10 percent inflation rate, is approximately 10.98 percent.