mcqs Math Simple Interest Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan. 8034

Question: Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 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) = $5600

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11200

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11200 – $5600 = $5600

Thus, Simple Interest = $5600

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5600}/_{5600 × 10}

= ⁵⁶⁰⁰⁰⁰/₅₆₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5600

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $5600 (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 = 10% of Principal

= 10% of $5600

= ¹⁰/₁₀₀ × 5600

= ^{10 × 5600}/₁₀₀

= ⁵⁶⁰⁰⁰/₁₀₀ = 560

Thus, simple Interest for 1 year = $560

Now,

∵ If the simple Interest is $560, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₀ years

∴ If the simple Interest is $5600, then the time = ¹/₅₆₀ × 5600 years

= ^{1 × 5600}/₅₆₀ years

= ⁵⁶⁰⁰/₅₆₀ = 10 years

Thus, time (T) = 10 years Answer