mcqs Math Simple Interest In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum? 7271

Question: In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?

(A)  3.75
(B)  6.25
(C)  5
(D)  7.5

Correct Answer 5

Solution And Explanation

Solution

Given,

Principal (P) = $3100

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

Amount (A) = $3875

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3875 – $3100 = $775

Thus, Simple Interest = $775

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 775}/_{3100 × 5}

= ⁷⁷⁵⁰⁰/₁₅₅₀₀

= 5 years (using formula)

Thus, Time (T) = 5 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $3100

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

Simple Interest = $775 (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 $775, then the time = ¹/₁₅₅ × 775 years

= ^{1 × 775}/₁₅₅ years

= ⁷⁷⁵/₁₅₅ = 5 years

Thus, time (T) = 5 years Answer