mcqs Math Simple Interest In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum? 7231

Question: In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

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

Correct Answer 3

Solution And Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3565

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3565 – $3100 = $465

Thus, Simple Interest = $465

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 465}/_{3100 × 5}

= ⁴⁶⁵⁰⁰/₁₅₅₀₀

= 3 years (using formula)

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

Here, we have

Principal (P) = $3100

Rate of Simple Interest (R) = 5% per annum

Simple Interest = $465 (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 = 5% of Principal

= 5% of $3100

= ⁵/₁₀₀ × 3100

= ^{5 × 3100}/₁₀₀

= ¹⁵⁵⁰⁰/₁₀₀ = 155

Thus, simple Interest for 1 year = $155

Now,

∵ If the simple Interest is $155, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₅₅ years

∴ If the simple Interest is $465, then the time = ¹/₁₅₅ × 465 years

= ^{1 × 465}/₁₅₅ years

= ⁴⁶⁵/₁₅₅ = 3 years

Thus, time (T) = 3 years Answer