mcqs Math Simple Interest Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan. 7293

Question: Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.

(A)  4.5
(B)  7.5
(C)  6
(D)  9

Correct Answer 6

Solution And Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8024

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8024 – $5900 = $2124

Thus, Simple Interest = $2124

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2124}/_{5900 × 6}

= ²¹²⁴⁰⁰/₃₅₄₀₀

= 6 years (using formula)

Thus, Time (T) = 6 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5900

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2124 (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 $5900

= ⁶/₁₀₀ × 5900

= ^{6 × 5900}/₁₀₀

= ³⁵⁴⁰⁰/₁₀₀ = 354

Thus, simple Interest for 1 year = $354

Now,

∵ If the simple Interest is $354, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₄ years

∴ If the simple Interest is $2124, then the time = ¹/₃₅₄ × 2124 years

= ^{1 × 2124}/₃₅₄ years

= ²¹²⁴/₃₅₄ = 6 years

Thus, time (T) = 6 years Answer