mcqs Math Simple Interest Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan. 7903

Question: Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 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) = $4900

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

Amount (A) = $7840

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7840 – $4900 = $2940

Thus, Simple Interest = $2940

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2940}/_{4900 × 6}

= ²⁹⁴⁰⁰⁰/₂₉₄₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $4900

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

Simple Interest = $2940 (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 $4900

= ⁶/₁₀₀ × 4900

= ^{6 × 4900}/₁₀₀

= ²⁹⁴⁰⁰/₁₀₀ = 294

Thus, simple Interest for 1 year = $294

Now,

∵ If the simple Interest is $294, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₉₄ years

∴ If the simple Interest is $2940, then the time = ¹/₂₉₄ × 2940 years

= ^{1 × 2940}/₂₉₄ years

= ²⁹⁴⁰/₂₉₄ = 10 years

Thus, time (T) = 10 years Answer