Question

Assertion (A): Sunidhi deposits ₹ 1600 per month in a bank for `1 1/2` years in a recurring deposit account at 10% p.a. She gets ₹ 31080 on maturity.

Reason (R): Maturity value is given by MV = (P × n) – S.I.

Options

• A is true, R is false

• A is false, R is true

• Both A and R are true

• Both A and R are false

Answer 1

A is true, R is false

Explanation:

Number of months = 1.5 years = 18 months.

Total deposited = 1600 × 18 = ₹ 28,800.

Interest on a recurring (monthly) deposit (simple interest) is `I = P xx [(n(n + 1))/(2 xx 12)] xx (r/100)`. 

Using P = 1600, n = 18, r = 10% gives

`I = 1600 xx ((18 × 19)/24) xx 0.10`

= ₹ 2,280

Maturity value = Total deposited + Interest

= 28,800 + 2,280

= ₹ 31,080

So, Assertion A is true.

Reason R is false because it states MV = (P × n) – S.I., which has the wrong sign; maturity value adds interest, it does not subtract it.