Question

Ankita started paying Rs 400 per month in a 3 year recurring deposit. After six months her brother Anshul started paying Rs 500 per month in 2.5 years recurring deposit. The bank paid 10 % simple interest for both. At maturity who will get more money and by how much ?
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Answer 1

Given :

Amount deposit by Ankita = Rs 400

Time period of deposition = 3 years = 12 × 3 = 36 months

Again

Amount deposit by Anshul = Rs 500

Time period of deposition = 2.5 years = 12 × 2.5 = 30 months

Rate of interest paid by bank = 10%

To Find :

At maturity who will get more money and by how much

Solution :

For Ankita

Principal deposit for 1 months = Amount deposit × $\dfrac{n(n+1)}{2}$

                                                   = Rs 400 × $\dfrac{36(36+1)}{2}$

                                                   = Rs 400 × 18 × 37

                                                   = Rs 266400

Now,

Interest = $\dfrac{principal \times Rate \times Time}{100}$

             = $\dfrac{266400 \times 10 \times 1}{100 \times 12}$

             = Rs 2220

So, Maturity Amount = Principal deposit for 1 months + Interest

                                   = Rs 266400 + Rs 2220

                                   = Rs 268620

Again

For Anshul

Principal deposit for 1 months = Amount deposit × $\dfrac{n(n+1)}{2}$

                                                   = Rs 500 × $\dfrac{30(30+1)}{2}$

                                                   = Rs 500 × 15 × 31

                                                   = Rs 232500

Now,

Interest = $\dfrac{principal \times Rate \times Time}{100}$

             = $\dfrac{232500 \times 10 \times 1}{100 \times 12}$

             = Rs 1937.5

So, Maturity Amount = Principal deposit for 1 months + Interest

                                   = Rs 232500 + Rs 1937.5

                                   = Rs 234437.5

From both calculation . Rs 234437.5 > Rs 232500

i.e Maturity Amount for Anshul is more than Maturity amount for Ankita.

.

Hence, The Maturity Amount for Anshul is more than Maturity amount for Ankita.     Answer

Answer 2

Step-by-step explanation:

In case of Ankita,

Deposit per month=Rs 400

Period (n) =3 years =36 months

Rate of interest=10%

Total principal for one month

=400×n(n+1) /2=400×36(36+1) /2

=400×36×37/2=Rs 266400

Interest=prl/100

=266400×10×1/100×12

=Rs 2220

so, amount of maturity =Rs 400×36+Rs2220

=Rs 14400+ Rs 2220=Rs 16620

In case of anshul

Deposit per month=Rs 500

Rate of intrest=10%

Period(n) =2 whole 1/2=30 months

Total principal of one month

=Rs 500×n(n+1) /2=500×30(30+1) /2

=Rs 500×30×31/2=Rs 232500

Intrest=232500×10×1/100×12=Rs 1937.50

Amount of maturity =Rs 500×30+Rs1937.50

=Rs 16937.50

At maturity Anshul will get more.

Difference=Rs 16937.50-Rs 16620.50

=Rs317.50

Hope it will help you..