mcqs Math Simple Interest Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan. 7515

Question: Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(A)  5.25
(B)  8.75
(C)  7
(D)  10.5

Correct Answer 7

Solution And Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9984

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9984 – $6400 = $3584

Thus, Simple Interest = $3584

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3584}/_{6400 × 8}

= ³⁵⁸⁴⁰⁰/₅₁₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $6400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3584 (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 = 8% of Principal

= 8% of $6400

= ⁸/₁₀₀ × 6400

= ^{8 × 6400}/₁₀₀

= ⁵¹²⁰⁰/₁₀₀ = 512

Thus, simple Interest for 1 year = $512

Now,

∵ If the simple Interest is $512, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₂ years

∴ If the simple Interest is $3584, then the time = ¹/₅₁₂ × 3584 years

= ^{1 × 3584}/₅₁₂ years

= ³⁵⁸⁴/₅₁₂ = 7 years

Thus, time (T) = 7 years Answer