mcqs Math Simple Interest In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum? 7241

Question: In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

(A)  3
(B)  5
(C)  4
(D)  6

Correct Answer 4

Solution And Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3472

Thus, time (T) = ?

Method (1) Using Formula

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3472 – $3100 = $372

Thus, Simple Interest = $372

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 372}/_{3100 × 3}

= ³⁷²⁰⁰/₉₃₀₀

= 4 years (using formula)

Thus, Time (T) = 4 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $3100

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $372 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 3% of Principal

= 3% of $3100

= ³/₁₀₀ × 3100

= ^{3 × 3100}/₁₀₀

= ⁹³⁰⁰/₁₀₀ = 93

Thus, simple Interest for 1 year = $93

Now,

∵ If the simple Interest is $93, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₃ years

∴ If the simple Interest is $372, then the time = ¹/₉₃ × 372 years

= ^{1 × 372}/₉₃ years

= ³⁷²/₉₃ = 4 years

Thus, time (T) = 4 years Answer