The matúrity value of
r.D. àccount is Rs.16176.if the monthly instàllment is Rs.400 and the rate of interest is 8% find the time of this R.D. account.
Answers
Given information to us:
- Maturity value (M.V.) of that account = Rs.16176
- Monthly instàllment = Rs.400
- Rate of interest = 8%
What's the need to be calculated:
- Time?
Calculations:
Here we have been given with the values of Maturity value, monthly instàllment and rate of interest. Monthly instàllment is the Principal (P). We have not been given with the value of time in months (n). So let us assume it be n months.
We have to use this formula for calculating the interest:
→ I = P × n(n+1)/2×12 × r/100
where,
- P denotes Principal
- n denotes number of months
- r denotes Rate of interest
Now we would be substituting values:
➟ I = 400 × n(n+1) × 8 / 2 × 12 × 100
Solving now:
➟ I = 4 × n(n+1) × 8 / 2 × 12
➟ I = n(n+1) × 8 / 2 × 3
➟ I = n(n+1) × 4 / 3
➟ I = 4n(n+1) / 3
We came to knew about the interest which had been taken. Using the formula for calculating Maturity value that is,
➟ Maturity value = P × n + Interest
Substituting values:
➟ Maturity value = 400 × n + 4n(n+1) / 3
Maturity value is Rs.16176 substituting it:
➟ 16176 = 400n + 4n² + 4
Cross multiplication of denominator 3 with 15176 and taking L.CM.:
➟ 48528 = 1200n + 4n² + 4n
➟ 48528 = 1204n + 4n²
➟ 0 = 4n² + 1204n - 48528
Now, by dividing all the terms by 4 we get:
➟ 0 = n² + 301n - 12132
➟ n² + 337n - 36n - 12132
➟ n(n + 337) - 36(n + 337)
➟ (n + 337) (n - 36)
Thus,
➟ n - 36 = 0
➟ n = 36
As we know that n is number of months now convert it into years:
➟ 1 year = 12 months
➟ 36 months = 3 years
Conclusion:
- Time of the R.D. account. is 3 years
Answer is in the attachment
