mcqs Math Simple Interest In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum? 7243

Question: In how much time a principal of $3200 will amount to $3584 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) = $3200

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

Amount (A) = $3584

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3584 – $3200 = $384

Thus, Simple Interest = $384

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 384}/_{3200 × 3}

= ³⁸⁴⁰⁰/₉₆₀₀

= 4 years (using formula)

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

Here, we have

Principal (P) = $3200

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

Simple Interest = $384 (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 $3200

= ³/₁₀₀ × 3200

= ^{3 × 3200}/₁₀₀

= ⁹⁶⁰⁰/₁₀₀ = 96

Thus, simple Interest for 1 year = $96

Now,

∵ If the simple Interest is $96, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₆ years

∴ If the simple Interest is $384, then the time = ¹/₉₆ × 384 years

= ^{1 × 384}/₉₆ years

= ³⁸⁴/₉₆ = 4 years

Thus, time (T) = 4 years Answer