Banking — Assertion-Reason Type Questions

A person deposit ₹P, every month for n months at R percent per annum, simple interest in a recurring deposit account.

Assertion (A): The maturity value is more than total amount deposited by the person.

Reason (R): Maturity value includes an interest equal to $\dfrac{\text{P} \times \text{n(n + 1)} \times \text{R}}{2400}$

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Answer

Given,

Amount deposited per month = ₹ P

Time = n months

Rate of interest = R%

The total amount deposited is the monthly deposit multiplied by the number of months.

Total deposited = P x n

The interest earned is given by the formula = $\text{P} \times\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{R}}{100}$

The maturity value is the total deposited amount plus the interest earned.

Maturity value = P x n + $\text{P} \times\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{R}}{100}$

The maturity value includes the total deposited amount plus the interest earned, which is a positive value.

∴ The maturity value is more than total amount deposited by the person.

So, assertion (A) is true.

By formula,

Interest = $\text{P} \times\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{R}}{100}$

= $\dfrac{\text{P} \times \text{n(n + 1)} \times \text{R}}{2400}$

So, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

Jena has a cumulative deposit account in Indian Bank. She deposit ₹ 500 per month for 2 years. Bank pays interest at the rate of 6% p.a.

Assertion (A): Money received by Jena at maturity is ₹ 12,750.

Reason (R): Maturity value = money deposit + interest earned.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Answer

Given,

P = ₹ 500/month

n = 2 years or 24 months

r% = 6%

By formula,

M.V. = money deposit + interest

So, reason (R) is true.

M.V. = P x n + P x $\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{r}}{100}$

Substituting the values, we get :

$M.V. = 500 \times 24 + 500 \times \dfrac{24(24 + 1)}{2 \times 12} \times \dfrac{6}{100}\\[1em] = 1200 + 500 \times \dfrac{24 \times 25}{24} \times \dfrac{6}{100}\\[1em] = 1200 + 500 \times 25 \times \dfrac{6}{100}\\[1em] = 1200 + 500 \times \dfrac{6}{4}\\[1em] = 1200 + 125 \times 6\\[1em] = 1200 + 750\\[1em] = ₹ 12,750$

So, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

Roohana has a recurring deposit account in State Bank of India. She deposits ₹ 800 per month for $2\dfrac{1}{2}$ years. Bank pays interest at the rate of 5% p.a.

Assertion (A): Interest earned by Roohana in $2\dfrac{1}{2}$ years is ₹ 1,650.

Reason (R): Interest earned = $P \times \dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{r}}{100}$

where, P = monthly instalment, n = number of installments and r = rate of interest p.a.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Answer

Given,

P = ₹ 800/month

n = $2\dfrac{1}{2}$ years or 30 months

r% = 5%

By formula,

I = P x $\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{r}}{100}$

So, reason (R) is true.

Substituting the values, we get :

$I = 800 \times \dfrac{30(30 + 1)}{2 \times 12} \times \dfrac{5}{100}\\[1em] = 800 \times \dfrac{30 \times 31}{24} \times \dfrac{5}{100}\\[1em] = 800 \times \dfrac{10 \times 31}{8} \times \dfrac{5}{100}\\[1em] = 10 \times 31 \times 5\\[1em] = ₹ 1,550.$

So, assertion (A) is false.

Thus, Assertion (A) is false, but Reason (R) is true.

Hence, option 2 is the correct option.