mcqs Math Simple Interest Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan. 8036

Question: Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 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) = $5800

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

Amount (A) = $11600

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11600 – $5800 = $5800

Thus, Simple Interest = $5800

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5800}/_{5800 × 10}

= ⁵⁸⁰⁰⁰⁰/₅₈₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5800

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

Simple Interest = $5800 (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 $5800

= ¹⁰/₁₀₀ × 5800

= ^{10 × 5800}/₁₀₀

= ⁵⁸⁰⁰⁰/₁₀₀ = 580

Thus, simple Interest for 1 year = $580

Now,

∵ If the simple Interest is $580, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₈₀ years

∴ If the simple Interest is $5800, then the time = ¹/₅₈₀ × 5800 years

= ^{1 × 5800}/₅₈₀ years

= ⁵⁸⁰⁰/₅₈₀ = 10 years

Thus, time (T) = 10 years Answer