Question

Reena made a fixed deposit for certain years. She deposited $3,120, and after maturity of the fixed deposit, she got $3,972. The interest rate was 10% p.a. compounded annually. Find the number of years Reena made the fixed deposit for.

a) 1 year
b) 2 years
c) 3 years
d) 4 years

Answer 1

Reena made the fixed deposit for approximately 3 years. The correct answer is option c) 3 years

Step-by-step explanation:

To find the number of years Reena made the fixed deposit for, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the final amount ($3,972)
• P is the principal amount ($3,120)
• r is the annual interest rate (10% or 0.10)
• n is the number of times the interest is compounded in a year (1, since it is compounded annually)
• t is the number of years

Plugging in the given values, we get:

$3,972 = $3,120(1 + 0.10/1)^(1 * t)

Dividing both sides by $3,120, we have:

(1 + 0.10)^t = $3,972/$3,120

Simplifying further, we get:

1.10^t ≈ 1.273

Taking the logarithm of both sides to isolate t, we get:

t ≈ log(1.273)/log(1.10)

Using a calculator, we find that t ≈ 3

Therefore, Reena made the fixed deposit for approximately 3 years (c).