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 $11520 to clear the loan, then find the time period of the loan. 7980

Question: Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(A)  7.5
(B)  12.5
(C)  10
(D)  15

Correct Answer 10

Solution And Explanation

Solution

Given,

Principal (P) = $6400

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

Amount (A) = $11520

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11520 – $6400 = $5120

Thus, Simple Interest = $5120

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5120}/_{6400 × 8}

= ⁵¹²⁰⁰⁰/₅₁₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $6400

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

Simple Interest = $5120 (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 $5120, then the time = ¹/₅₁₂ × 5120 years

= ^{1 × 5120}/₅₁₂ years

= ⁵¹²⁰/₅₁₂ = 10 years

Thus, time (T) = 10 years Answer