A sum needs to be repaid in two annual instalments of $2227$ and $2023$ rs., given the rate of interest as 19%, then the problem is to find what sum was borrowed at the starting of first year.
The way I solved it is like this:
$Total Amount=2227+2023= 4250$
$Rate= 19%$
$Time= 2 years$
We know the instalments are based on the concept of compound interest, so, applying below formula
$4250=P(1+\frac{19}{100})^2$
I get Sum as $3000$ approx., Which is incorrect. The correct result is $3300$. Can anyone help me to understand how and why my method is giving incorrect result.
Thanks.
We need the equality of the present value of the borrowed money $C_0$ and the present value of the two installments $I_1$ and $I_2$. I assume that the first installment is paid at the end of the first year. Thus the present value of it is $ \frac{I_1}{1.19^1}= \frac{2227}{1.19^1}$. It has to be discounted only once. And the present value of the second istallment is $ \frac{I_2}{1.19^2} =\frac{2023}{1.19^2}$. The sum then is $C_0$.