Question

Teddy invested 89000 USD in an account that pays a nominal annual interest rate of 9%, compounded monthly. This amount is invested for 6 years and the inflation rate in these 6 years is i%. Find the real interest rate per year, giving the answer in terms of i

Answer 1

To find the real interest rate per year, calculate the nominal interest earned using the compound interest formula and adjust for the inflation rate.

Step-by-step explanation:

To find the real interest rate per year, we need to calculate the nominal interest earned and adjust for the inflation rate.

First, let's calculate the nominal interest earned. Since the interest is compounded monthly, we need to use the compound interest formula:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal amount, r is the nominal interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we have:

A = 89000(1 + 0.09/12)^(12*6)

Next, we need to adjust for the inflation rate. The real interest rate can be calculated using the formula:

Real Interest Rate = Nominal Interest Rate - Inflation Rate

Substituting the values, we have:

Real Interest Rate = 0.09 - (i/100)

So, the real interest rate per year is 0.09 - (i/100).