mcqs Math Simple Interest Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan. 7912

Question: Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 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) = 6% per annum

Amount (A) = $9280

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9280 – $5800 = $3480

Thus, Simple Interest = $3480

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3480}/_{5800 × 6}

= ³⁴⁸⁰⁰⁰/₃₄₈₀₀

= 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) = 6% per annum

Simple Interest = $3480 (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 = 6% of Principal

= 6% of $5800

= ⁶/₁₀₀ × 5800

= ^{6 × 5800}/₁₀₀

= ³⁴⁸⁰⁰/₁₀₀ = 348

Thus, simple Interest for 1 year = $348

Now,

∵ If the simple Interest is $348, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₈ years

∴ If the simple Interest is $3480, then the time = ¹/₃₄₈ × 3480 years

= ^{1 × 3480}/₃₄₈ years

= ³⁴⁸⁰/₃₄₈ = 10 years

Thus, time (T) = 10 years Answer