mcqs Math Simple Interest Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan. 7993

Question: Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 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) = $4600

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8740

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8740 – $4600 = $4140

Thus, Simple Interest = $4140

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4140}/_{4600 × 9}

= ⁴¹⁴⁰⁰⁰/₄₁₄₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $4600

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4140 (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 = 9% of Principal

= 9% of $4600

= ⁹/₁₀₀ × 4600

= ^{9 × 4600}/₁₀₀

= ⁴¹⁴⁰⁰/₁₀₀ = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₄ years

∴ If the simple Interest is $4140, then the time = ¹/₄₁₄ × 4140 years

= ^{1 × 4140}/₄₁₄ years

= ⁴¹⁴⁰/₄₁₄ = 10 years

Thus, time (T) = 10 years Answer