Question

Emma has taken out a loan of $ 2,000,000. She pays $ 11,000 a month. This amount only covers the interest on her loan, so she continues to owe the bank $ 2,000,000. What is the simple annual interest rate? After paying a monthly installment of $ 11,000 for 20 years, she repays the loan. How many dollars has she paid in 20 years?

Answer 1

We are given the Principal(P) = $2,000,000, Interest(I) = $11,000 for a month(T) = 1/12 Years;

From the question, we are asked to find the Simple Interest Rate;

Recall that

$SI=P\times R\times T$

If we make R the subject of formula, we would get;

$R=\frac{SI}{P\times T}$

substituting the values of SI, P and T, we would get;

$R=\frac{11000}{2000000\times\frac{1}{12}}=6.6\%$

following the question further, Emma made the payment of $11000 monthly(let's take that as the new Simple Interest) for 20 years(which is the new T). If we use the rate R = 6.6%, we can use the formula for SImple Interest to calculate to calulate the Principal.

That is, if

$\begin{gathered} SI=P\times R\times T \\ P=\frac{SI}{R\times T} \end{gathered}$

substituting the values of SI, R, and T, we would get;

$P=\frac{11000}{\frac{6.6}{100}\times20}=8333.33$

We can conclude that Emma has paid $8333.33 for 20 years.