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 $$A(0)(1+0.06)^{4.5}=20000$$ $$A(0)=\frac{20000}{1.06^{4.5}}=15386.99$$