mcqs Math Simple Interest In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum? 7225

Question: In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(A)  2.25
(B)  3.75
(C)  3
(D)  4.5

Correct Answer 3

Solution And Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3416

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3416 – $3050 = $366

Thus, Simple Interest = $366

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 366}/_{3050 × 4}

= ³⁶⁶⁰⁰/₁₂₂₀₀

= 3 years (using formula)

Thus, Time (T) = 3 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $3050

Rate of Simple Interest (R) = 4% per annum

Simple Interest = $366 (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 = 4% of Principal

= 4% of $3050

= ⁴/₁₀₀ × 3050

= ^{4 × 3050}/₁₀₀

= ¹²²⁰⁰/₁₀₀ = 122

Thus, simple Interest for 1 year = $122

Now,

∵ If the simple Interest is $122, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₂ years

∴ If the simple Interest is $366, then the time = ¹/₁₂₂ × 366 years

= ^{1 × 366}/₁₂₂ years

= ³⁶⁶/₁₂₂ = 3 years

Thus, time (T) = 3 years Answer