Ankita started paying Rs. 400 per month in a 3 year recurring deposit account. After six months her brother Anshul started paying Rs. 500 per month in a $2 \frac{1}{2}$ years recurring deposit. The bank paid 10% p.a. simple interest for both. At maturity who will get more money and by how much?

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Solution

Step 1: Given data
Given data for Ankita:
Installments per month, $(P) = Rs . 400$
Rate of Interest, $(R) = 10 % p . a .$
Time, $(n) = 3$ Years
Convert years into months.
$n = 3 = 3 \times 12 (∵ 1 year = 12 months) = 36 So, n = 36 months$
Given data for Anshul:
Instalments per month, $(P) = Rs . 500$
Rate of Interest, $(R) = 10 % p . a .$
Time, $(n) = 2 \frac{1}{2}$ Years
Convert years into months.
$n = 2 \frac{1}{2} = \frac{5}{2} = \frac{5}{2} \times 12 (∵ 1 year = 12 months) = 30 So, n = 30 months$
Step 2: Calculate maturity value
Calculate Ankita's maturity value.
$Maturity value = [1 + \frac{(n + 1) R}{2400}] \times n \times P = [1 + \frac{(36 + 1) \times 10}{2400}] \times 36 \times 400 = [1 + \frac{37 \times 10}{2400}] \times 36 \times 400 = [1 + \frac{370}{2400}] \times 36 \times 400 = [1 + \frac{370}{2400}] \times 14400 = [\frac{2400 + 370}{2400}] \times 1200 = [\frac{2770}{2400}] \times 14400 = Rs . 16620$
The maturity amount received by Ankita is $Rs . 16620$ .
Calculate Anshul's maturity value.
$Maturity value = [1 + \frac{(n + 1) R}{2400}] \times n \times P = [1 + \frac{(30 + 1) \times 10}{2400}] \times 30 \times 500 = [1 + \frac{31 \times 10}{2400}] \times 30 \times 500 = [1 + \frac{310}{2400}] \times 30 \times 500 = [1 + \frac{310}{2400}] \times 15000 = [\frac{2400 + 310}{2400}] \times 15000 = [\frac{2710}{2400}] \times 15000 = Rs . 16937.5$
The maturity value of Anshul is $Rs . 16937.5$ .
Step 3: Comparing maturity value of Ankita and Anshul
Ankita's maturity value is $Rs . 16620$ and Anshul's maturity value is $Rs . 16937.5$ .
Hence, Anshul will get more amount at maturity.
$Difference = 16937.50 - 16620 = Rs . 317.50$
Hence, the difference between Ankita's and Anshul's maturity value is $Rs . 317.50$ .

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Ankita started paying Rs. 400 per month in a 3 year recurring deposit account. After six months her brother Anshul started paying Rs. 500 per month in a 212 years recurring deposit. The bank paid 10% p.a. simple interest for both. At maturity who will get more money and by how much?

Ankita started paying Rs. 400 per month in a 3 year recurring deposit account. After six months her brother Anshul started paying Rs. 500 per month in a $2 \frac{1}{2}$ years recurring deposit. The bank paid 10% p.a. simple interest for both. At maturity who will get more money and by how much?