mcqs Math Simple Interest In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum? 7268

Question: In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

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

Correct Answer 5

Solution And Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3840

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3840 – $3200 = $640

Thus, Simple Interest = $640

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 640}/_{3200 × 4}

= ⁶⁴⁰⁰⁰/₁₂₈₀₀

= 5 years (using formula)

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

Here, we have

Principal (P) = $3200

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

Simple Interest = $640 (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 $3200

= ⁴/₁₀₀ × 3200

= ^{4 × 3200}/₁₀₀

= ¹²⁸⁰⁰/₁₀₀ = 128

Thus, simple Interest for 1 year = $128

Now,

∵ If the simple Interest is $128, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₈ years

∴ If the simple Interest is $640, then the time = ¹/₁₂₈ × 640 years

= ^{1 × 640}/₁₂₈ years

= ⁶⁴⁰/₁₂₈ = 5 years

Thus, time (T) = 5 years Answer