mcqs Math Simple Interest In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum? 7232

Question: In how much time a principal of $3150 will amount to $3622.5 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) = $3150

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

Amount (A) = $3622.5

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3622.5 – $3150 = $472.5

Thus, Simple Interest = $472.5

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 472.5}/_{3150 × 5}

= ⁴⁷²⁵⁰/₁₅₇₅₀

= 3 years (using formula)

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

Here, we have

Principal (P) = $3150

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

Simple Interest = $472.5 (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 $3150

= ⁵/₁₀₀ × 3150

= ^{5 × 3150}/₁₀₀

= ¹⁵⁷⁵⁰/₁₀₀ = 157.5

Thus, simple Interest for 1 year = $157.5

Now,

∵ If the simple Interest is $157.5, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/_157.5 years

∴ If the simple Interest is $472.5, then the time = ¹/_157.5 × 472.5 years

= ^{1 × 472.5}/_157.5 years

= ^472.5/_157.5 = 3 years

Thus, time (T) = 3 years Answer