mcqs Math Simple Interest In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum? 7253

Question: In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?

(A)  3
(B)  5
(C)  4
(D)  6

Correct Answer 4

Solution And Explanation

Solution

Given,

Principal (P) = $3200

Rate of Simple Interest (R) = 5% 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 × 5}

= ⁶⁴⁰⁰⁰/₁₆₀₀₀

= 4 years (using formula)

Thus, Time (T) = 4 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $3200

Rate of Simple Interest (R) = 5% 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 = 5% of Principal

= 5% of $3200

= ⁵/₁₀₀ × 3200

= ^{5 × 3200}/₁₀₀

= ¹⁶⁰⁰⁰/₁₀₀ = 160

Thus, simple Interest for 1 year = $160

Now,

∵ If the simple Interest is $160, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₆₀ years

∴ If the simple Interest is $640, then the time = ¹/₁₆₀ × 640 years

= ^{1 × 640}/₁₆₀ years

= ⁶⁴⁰/₁₆₀ = 4 years

Thus, time (T) = 4 years Answer