# Compounded discount rate

The total amount of a loan to which interest has been added is $20000$. The term of the loan was for $4.5$ years. If the annual rate of interest was $6\%$ and interest was compounded annually, what was the amount of the loan? The answer is $15 386.99$

The interest after $4.5$ years is given as

$$0.06^{4.5}A(0)$$

Then to calculate the amount of loan,

$$A(0)+0.06^{4.5}A(0)=20000$$

The answer for $A(0)$ does not come out.

There is an error in the formula used. The correct expression is $$A(0)(1+0.06)^{4.5}=20000$$ $$A(0)=\frac{20000}{1.06^{4.5}}=15386.99$$