A loan of \$10 000 repaid over a period of $n$ years at $r$% per year satisfies the equation $$ 10000 = \frac{x}{\left(1+\frac{r}{100}\right)}+\frac{x}{\left(1+\frac{r}{100}\right)^2}+\frac{x}{\left(1+\frac{r}{100}\right)^3}+\cdots++\frac{x}{\left(1+\frac{r}{100}\right)^n} $$ where $x$ is the repayment installment. Find $x$ in terms of $r$ and $n$ and compute its value if $r$ = 10 and $n$ = 20.
I've been doing loads of series exercises but this one now has more than 1 variable and now I feel stumped. How do you get started with this?
This is not a p-series because the numerator is not 1? Based on the next question this might be a harmonic series...
Any assistance would be great.
Thanks