Question

The maturity value of a R.D. Account is Rs 16,176. If the monthly instalment is Rs 400 and the rate of interest is 8%; find the time (period) of this R.D. Account.

Answer 1

P=rs.400
n=n
r=8%p.a.

S.I = $P\times \frac{n(n+1)}{2\times 12}\times \frac{r}{100}$

$=400\times \frac{n(n+1)}{2\times 12}\times \frac{8}{100}$

$=400\times \frac{n(n+1)}{24}\times \frac{8}{100}$

$=\frac{4n(n+1)}{3}$

maturity value = $(400\times n)+\frac{4n(n+1)}{3}$

given maturity value= Rs. 16,176
then

$400n+\frac{4n(n+1)}{3}=16,176$

$1200n+4n^2+4n=48,528$

$4n^2+1204n=48,528$

$n^2+301n-12132=0$

$n^2+(337-36)n-12132=0$

$n^2+337n-36n-12132=0$

$n(n+337)-36(n+337)=0$

$(n+337)(n-36)=0$

$n=-337or36$

then no of months = 36 months = 3 years

Answer:- 36 months = 3 years