mcqs Math Simple Interest In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum? 7256

Question: In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% 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) = 2% per annum

Amount (A) = $3410

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3410 – $3100 = $310

Thus, Simple Interest = $310

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 310}/_{3100 × 2}

= ³¹⁰⁰⁰/₆₂₀₀

= 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) = 2% per annum

Simple Interest = $310 (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 = 2% of Principal

= 2% of $3100

= ²/₁₀₀ × 3100

= ^{2 × 3100}/₁₀₀

= ⁶²⁰⁰/₁₀₀ = 62

Thus, simple Interest for 1 year = $62

Now,

∵ If the simple Interest is $62, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂ years

∴ If the simple Interest is $310, then the time = ¹/₆₂ × 310 years

= ^{1 × 310}/₆₂ years

= ³¹⁰/₆₂ = 5 years

Thus, time (T) = 5 years Answer